This bug has been known for a long time.
I have made a comprehensive list about this issue.
Let’s be clear here, this issue is not only affecting the Pet Rescue Event, but all the others as well.
Of course, you can get much more battles when this bug is triggered, but I usually just exit the game to avoid any issues.
I noticed that it also helps if you completely disable the Chat, and exit it.
I think that this is somehow connected to this issue at hand.