Mine seem to take about 24 hours (maybe just a little longer) to have them all. I can often find one or two, and then the next day find many more. Right now I have somewhere between 18-25 fry swimming around and they have been there for about 5 days now so I am assuming they are here to stay. The first batch I only found 4. My tank was planted then but not nearly as heavily as it is now, so I guess that explains the large number.
My platy is HUGE too. When she is about to give birth she looks like she is going to burst; but even afterwards she's a little fatty.