I don't have Platy, but I've had many guppies born in my tanks. I've seen them drop anywhere from 20+ fry within a very short time, and also had them have 2-3 fry every day or so for a week or so. From what I've read, this is normal, and can depend on many factors (age of the fish, how many broods she has had, water conditions, etc). Personally, I don't separate live bearers for birth anymore. With some fish, it seems to stress them out to be contained (my mollies are like this), with others (guppies) the fry seem to have a higher survival rate staying in the main tank with lots of floating plants until I can 'rescue' them, and plop them into a breeder basket or a grow out tank. Maybe it's just MY guppies - but they're voracious, and seem to find it much easier to eat their young when they're in a more confined place!
Good luck with your babies!