You might want to make sure that all water parameters are in the ideal range (temp, ph, ammonia, nitrite, nitrate, etc). In adverse conditions platies may survive, but they willl cut back on the frequency and number of fry in each batch. Make sure that all the fish are healthy, and properly fed. Over feeding will pollute the water, but under feeding will stunt their growth and fertility.
Also make sure that both of your types of platies are the same species, Although hybrids are possible most tend to prefer their own species and will only mate with a closely related species as a last resort.
I have read that many of the odd fin shaped variations of livebearers have difficulty mating especially males with a shape distorted gonopodium (anal fin).
A small male that is getting bullied by other fish is usually too busy hiding to mate. The same is true of all the fish if they are regularly frightened. My platies are not shy and will mate for an audience.
Be absolutely sure that you have 4 females and 2 males, sometimes due to slow or late developement they are tough to tell apart.
Power filters have a tendancy to suck up fry (check the filter for any).
Make sure there are lots of places for fry to hide and not just a few here and there.
Look real close regularly, many newborn platy fry are almost translucent and only a few millimeters long (they like to hide and can move suprizingly quick).
If all of the above is good to go I see no reason you shouldn't have more than you know what to do with in a short period of time.