You might want to look away.
People! The verb "may" is present tense. It's an auxialiary verb . . . and did I mention it's present tense?!
The inflected past tense form is "might."
That's right: "may" is present, immediate, happening now. "Might" is past tense, done been done as one of my most-beloved students is wont to say.
So what does that mean and why does anyone care?
Well, if you're writing in the past tense. And oh, it seems like 90+% of romantic fiction is in the past tense (present tense is pretty darn hard to maintain for an extended period, kinda like the second person) you cannot have sentences like, "It may have been a while . . ." or "He may not need . . ." Those are unnecessary tense shifts.
That. Is. Bad.
Might, people, if you're writing in the past tense. Might!
Thank you. You may return to your regularly scheduled blog-hopping now.