I don't think you have the proper approach to your issue.
Typically, if a game starts to go slower and slower, it's because you add stuff to it over time and it's not able to process everything in a timely fashion. If there is too much stuff from the beginning, the frame rate will be low but constant from the beginning.
Even if "pausing" a game to "let the frame rate catch up" or to "restore the FPS" seems to work to solve your current issue, it will not fix the underlying problem. It is not a good solution and your players will really not like that.