Discounted pizzas and financial aid for franchisees aren't doing much to curb Papa John's sales woes.

According to recent checks by Stifel, Papa John's same-store sales remain under pressure in the third quarter and, if they do not improve, store closures won't be far behind.

In July, same-store sales at the beleaguered pizza chain plunged 10.5 percent after it came to light that Papa John's founder had used a racially charged slur on a conference call. That trend continued in August.

So far in the third quarter, same-store sales are estimated to be down 10 to 11 percent, according to analyst Chris O'Cull.

"We are surprised the company's aggressive promotions the past several weeks have not curtailed the sales declines and we believe if the trend persists that it could lead to accelerating store closures during the next six months," O'Cull wrote in a research note Thursday.

O'Cull predicts that between 150 and 250 restaurants in noncore markets, the West Coast and Northeast, could be in danger of shuttering if Papa John's is unable to reignite its sales.

And store closures would have much bigger implications than just lost royalty revenue. Papa John's relies heavily on its in-house commissary sales, what it charges franchisees for ingredients. In the first half of the year, these sales represented about 35 percent of Papa John's profits.

With fewer locations, Papa John's may be forced to raise its commissary prices in order to make up the difference. However, franchisees are already struggling because of the weaker sales and are currently receiving assistance from the company in the manner of reduced royalties, fees and commissary prices.

Papa John's runs the risk of shuttering more stores if franchisees are unable to pay for ingredients.

"We concede new branding, marketing and value efforts, which are expected to debut in the [fourth quarter], could help stabilize the fundamentals, thus limiting the need for some franchisees to close units," O'Cull said. "There is also the possibility management could extend franchisee financial assistance measures to next year."

As consumers flee Papa John's, a big piece of the more than $41 billion quick-service pizza category is ripe for the taking — and it's up to Domino's and Pizza Hut to seize the opportunity.

In 2017, Domino's controlled 14.2 percent of pizza sales, according to a report by Mark Kalinowski, CEO of Kalinowski Equity Research. Pizza Hut had 13.2 percent of the market, and Papa John's held onto 7.2 percent.

By the end of 2018, Kalinowski forecasts that Domino's market share will surpass 15 percent and Papa John's will slip below 7 percent. He said that Pizza Hut's market share would remain flat.

Data from Earnest Research suggests that Papa John's has lost about 5 percent of its market share to Domino's and Pizza Hut since October 2017, when Schnatter made disparaging comments about how the National Football League handled player protests that occurred during the national anthem.

Representatives for Papa John's did not immediately respond to CNBC's request for comment.