For four months, Yitzchok Shuster felt secure in the knowledge that he had signed up for a health insurance plan on New York’s Affordable Care Act exchange, and that he was still able to see his longtime doctor, who was employed by the Mount Sinai Health System.

After his insurance took effect in January, he visited the doctor, Gary Lerner, at his Forest Hills, Queens, office three or four times with minor ailments. Then at his last visit, three weeks ago, Mr. Shuster was warned that the practice was planning to drop his plan, Empire BlueCross BlueShield Pathway.

“The girl at the front desk, a real sweetheart, she told me, Yitzchok, I really don’t want to burst your bubble because we told you that they would be taking your plan,” Mr. Shuster, 52, said Thursday. “But we have it from on high that in a month or two, they’re not going to be.”

A Mount Sinai cancer patient, who asked to be identified only as Beth because she was afraid her doctors would resent her if they knew she was complaining, said she visited her Manhattan doctor, Stacy Suden, on March 24 without incident. But said she was told on Tuesday that Dr. Suden was no longer taking her insurance, MetroPlus.