Mei Xiang, the National Zoo’s female giant panda, has entered the final phase of her reproductive cycle — one that could mark the end of her stay in Washington, the zoo announced Monday.

Panda watchers now have 40 to 50 days to see if she produces a cub.

This could be Mei’s last chance to do so here. The zoo badly wants panda cubs and China, which owns and leases all giant pandas in U.S. zoos, has said it would consider replacing Washington’s pandas if Mei fails to become pregnant this year.

It is notoriously hard to determine if a giant panda is pregnant, the zoo says, because the animal can exhibit many false signs of pregnancy. Mei has had five consecutive false pregnancies since 2007.

“Mei Xiang returned to a more normal estrous cycle this year,” the zoo said in a statement. “She went into heat in April after three consecutive years of going into heat in January.”

She was artificially inseminated on April 29 and 30 after she and the zoo’s male giant panda, Tian Tian, failed to mate on their own.

The two have produced only one cub, Tai Shan, in the more than 10 years they have been at the zoo. Tai Shan, who was born in 2005, was sent to a breeding program in China in 2010.

In its quest for cubs, the zoo has focused intense research on panda reproduction. And last December local philanthropist David M. Rubenstein, co-founder and managing director of the Carlyle Group, a global asset-management firm, pledged $4.5 million to fund such research.

The zoo has said that the chances of Mei, 14, becoming pregnant after years of failed attempts may be less than 10 percent.

For his part, Tian Tian, who turns 15 next Monday, has proved to be a clueless breeder with flawed technique. In addition, his genes are not that valuable because his father has sired dozens of offspring in the captive population.

Ideally, the zoo would like both pandas replaced. But if only one can be swapped, the zoo has said it should be the female, whose chances of reproducing are probably nearing zero.

Last year, Chinese and U.S. officials agreed to extend the pandas’ stay in Washington for five more years. The agreement replaced a 10-year lease that expired Dec. 6, 2010. The new agreement expires Dec. 6, 2015.

The zoo has said in order to open replacement discussions with China, it would have to demonstrate all the work that has been done to try to produce cubs in Washington and then request new pandas.