How many times should one proofread their paper before submission?
There is no global constant q such that more than q proofreads are required. It depends on your writing style, the topic, your mood and many many other factors.

A comment though: In my experience, no matter how many times you personally proofread the paper, there are cases where it is not enough and you need a second or a third person to proofread your paper to catch mistakes for which you have a blind spot (i.e., no matter how many times you read you won't be able to catch the subtle mistakes and this is more true if you are not native english speaker or you are younger researcher.)