I think you need to figure out why this is happening. Can you reproduce the behavior by creating a
daemon app and letting it run in the background? Do other games respond the same way exactly? If not then why is your game slowing down so dramatically is the question and it's a debug question.
- If you let the game continue as normal, it will probably highly increase the chances that the player will lose the game. This will cause frustration.
- If you pause the game automatically it will possibly disrupt the player.
What you could consider is accepting more vague and inaccurate input from the user as correct input during this lag and when it occurs.
For instance, if the play had to touch the screen on the left between 7.3 and 7.7 seconds into the stage the give the player a wider time frame. This is hard to do but I feel it is more suitable than the other two options namely doing nothing & pausing.
Alternatively, you could simply slow down the gameplay pace when framerate drops beyond a certain point like under 30fp, you could slow down the gameplay according to the fps rate.