New Delhi (CNN) Is India distancing itself from the Tibetan exile community six decades after the Dalai Lama fled to the country?

That's the question many are asking after celebrations to mark the 60th anniversary of the spiritual leader's arrival in India have been moved or canceled, as Beijing and New Delhi seek to reboot ties in the wake of a tense year in bilateral relations.

From March 31, Tibetans in India are holding a year-long "Thank You India" event as a prelude to celebrating the Dalai Lama's time in the country and to show gratitude to the Indian government and its people for their support of Tibetan refugees.

But what should have been a moment of joy has been overshadowed by a flurry of speculation about the future of the exiled Tibetan community -- and especially the freedom they have enjoyed in India since the late 1950s.

"It looks like the Government of India is changing its policy," said Claude Apri, an India-based expert on Tibet and author of several books on Tibetan issues.

After an unsuccessful revolt against the Chinese occupation of Tibet, the 14th Dalai Lama, Tibet's spiritual leader, fled the capital Lhasa in secret.

He crossed into India on March 31, 1959 and has made India his home ever since.

A living god-like figure for millions of Buddhists, India officially calls him "the most esteemed and honored guest of India." China accuses of him of being a "a wolf in monk's robes," engaged in "anti-China separatist activities under the cloak of religion with the aim of breaking Tibet away from China."

Photos: The Dalai Lama begins his exile The Dalai Lama, Tibet's spiritual leader, sits under a canopy in Mussoorie, India, on May 19, 1959. It was the first time he had posed for photographers since fleeing from the Chinese army in March of that year. China invaded Tibet in 1950, making historical claims on the region. Hide Caption 1 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama is seen with his mother outside the Birla House, his residence in Mussoorie. In 1960 he moved to Dharamsala, India, which remains his home today. Hide Caption 2 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama is actually the 14th Dalai Lama and the 74th manifestation of Avalokiteshvara Bodhisattva, the enlightened Buddha of compassion. During his life, he has traveled to numerous countries with a message of tolerance and peace. He won the Nobel Peace Prize in 1989. Hide Caption 3 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama's mother and his younger brother Ngari Rimpoche are photographed at the Birla House. Hide Caption 4 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama comes out of his house to address a religious congregation on May 22, 1959. He was 24 years old. Hide Caption 5 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama celebrates Buddha's birthday in Mussoorie. Hide Caption 6 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama sits under a portrait of Buddha as he gives an address at the Birla House. Leading Tibetan monks sit on his left. His tutors sit on his right. During his address, the Dalai Lama expressed hope that the strife in his country was only a passing phase, and he urged the gathering to pray for a return of peace to Tibet. Hide Caption 7 of 9 Photos: The Dalai Lama begins his exile The Dalai Lama was just 15 when he became Tibet's head of state and government in 1950. From 1954-1959, he participated in unsuccessful peace talks with Chinese leaders. Hide Caption 8 of 9 Photos: The Dalai Lama begins his exile Indian Prime Minister Jawaharlal Nehru visits the Dalai Lama at the Birla House. Hide Caption 9 of 9

'Very sensitive'

attending events planned by exiled Tibetans in India. In early March, news emerged that the Indian Foreign Secretary penned a classified advisory asking senior leaders and government officials to refrain fromattending events planned by exiled Tibetans in India.

The note reportedly said the events, in March and April, came at a "very sensitive time in the context of India's relations with China."

A week later, the Tibetan Central Administration -- the government in exile -- decided to move a major cultural event that was originally planned to be held in the Indian capital New Delhi with a speech by the Dalai Lama, to Dharamsala, where the exiled community is based.

A Dalai Lama-led inter-faith prayer ceremony was also scrapped, the Tibetan Central Administration said, as was the Seventh World Parliamentarians Convention on Tibet that was meant to be held on April 26-28 in Delhi.

The Tibetan Parliament-in-exile, the organizers of the convention, declined to give a reason for the cancellation of the high-profile event.

Sonam Dagpo, a spokesman for the Tibetan Central Administration said that there has been no direct communication from the Indian authorities and that the plans were changed out of respect to the Indian government's position.

"Once we (heard about the note), we decided to shift the venue," he said. "There are no ill feelings. If you weigh what the Indian government has done for us, that is far more than this."

The Indian foreign ministry issued a statement this month saying there is no change in India's position, and that "His Holiness is accorded all freedom to carry out his religious activities in India."

According to the latest data from the government in exile, more than 128,000 Tibetans live outside of their homeland. Of those, 94,000 live in India, around three quarters of the total. Another 10.6% live in Nepal and the remaining have resettled in more than 30 countries around the world.

Since 1974, the Dalai Lama has said he does not seek independence from China for Tibet, but a "meaningful autonomy" which would allow Tibet to preserve its culture and heritage.

India maintains that Tibetans in India "do not conduct political activities from Indian soil."

Dance, not fight

Recent statements from Beijing and Delhi show the two governments are seeking to mend ties after a turbulent year in bilateral relations.

Last year, troops from both countries were involved in a months-long border standoff in Doklam , up in the Himalayas near Bhutan.

At a press conference last month, Chinese Foreign Minister Wang Yi said the two countries leaders "have developed a strategic vision for the future of our relations: the Chinese 'dragon' and the Indian 'elephant' must not fight each other, but dance with each other."

India's Foreign Secretary Vijay Gokhale visited Beijing in February, where he said both sides noted the need to "address differences on the basis of mutual respect and sensitivity to each other's concerns, interests and aspirations."

Manoj Joshi, a fellow at the Observer Research Foundation, said India is keen to keep ties balanced, especially with China growing closer to rival Pakistan.

"Relations stand at an uneasy place, with India trying to backtrack somewhat and mend fences that were broken in the last two years," he told CNN.

He added China was also seeking progress as it didn't want "India to drift back into the American camp."

Indian Prime Minister Narendra Modi and Chinese President Xi Jinping are expected to meet on the sidelines of the Shanghai Cooperation Organization summit in June.

Tibetans may be the big losers if India and China do mend things up, said Tshering Chonzom Bhutia, associate fellow at the Institute of Chinese Studies in New Delhi.

"If policymakers in India continue to be guided by the perception that serving up the Tibet issue on the diplomatic plate to China is the most efficient way to improve India-China relations, then we can anticipate more restrictions on Tibetan activities in India," she said.

Against the backdrop of China's rising dominance in India's neighboring countries, Tibet is a minor issue for Delhi, said Tsering Shakya, a Tibet scholar and research chair at the University of British Columbia in Canada.

"India is sensing Tibet's appeal in the West is declining," Shakya said, freeing Delhi to play to Beijing's feelings on the issue.

Uncertainty

Adding to all this uncertainty is the confusion of what happens after the Dalai Lama dies.

In 2011, in a move to democratize the system of government, the Dalai Lama gave up his political and administrative powers and chose to remain as just a spiritual leader, but he is still far and away the community's most influential figure.

When the current Dalai Lama dies, Tibetans will be in a state of disarray, said Phunchok Stobdan, a former Indian diplomat and a senior fellow at the Institute for Defence Studies and Analyses in New Delhi, although he stressed that India will continue to support the Tibetan refugees on humanitarian grounds.

"India will do (this) because India is a democratic country. That is separate from the political side of it," he said.

But many Tibetans in India are concerned about their future in the country when the most influential figure in their community is no longer there to speak out on their behalf.

Ultimately, what might matter most is geopolitics.

"How the political issue of Tibet will pan out in the post-Dalai Lama era depends to a huge extent on the bilateral India-China dynamics as well as the regional and global situation," Bhutia said.