Just thought I'd share my admittedly brief experience, as I've raised about 50 livebearer fry (mollies, platies, and guppies) and have yet to have a death with my current setup.
I have a 26 gallon main tank that is almost exclusively livebearers (aside from some snails and otocinclus) and a 5.5 gallon tank I've set up for the fry. The 5.5 gallon has its own 100GPH HOB filter (with a prefilter sponge on the intake to keep the fry from being sucked up), 6 inch bubble wall, fairly thin layer of sand substrate, some rocks for decoration/shelter and a lot of Anacharis plants left free floating (they started out as a single batch and have grown considerably).
I feed 2 to 3 times per day, usually Hikari First Bites but I supplement that with crushed flake food, crushed freeze dried blood worms, and freeze dried brine shrimp. I've started feeding frozen blood worms recently, and they seem to like that as well. The latter foods seem more important as the fry grow larger, the younger fry generally don't go for it. I heavily overfeed relative to the size/number of fry. There is pretty much always some food in the tank. But I think the amount is still low enough that my filter (which at 100GPH is somewhat overkill for a 5.5 gallon tank) has no trouble cleaning up the ammonia from the excess food.
I change about 40% of the water every 5 days to 1 week. With water changes I use Prime for my water conditioner, add aquarium salt, and add Tetra FloraPride for the plants. I've also used API's StressZyme, but I really don't know how much difference, if any, that has made. My water is fairly alkaline out of the tap, the PH at 8. With my first batch of fry I was worried about the PH being too high and I mixed that with some bottled spring water, but I've since switched entirely to tap water and the fry seem fine either way. My ammonia and nitrite levels are nonexistent and the nitrate seems almost nonexistent too (maybe thanks to the Anacharis), though I don't monitor these regularly as long as everything seems healthy. I also have a single snail in the tank. I'm not sure where he came from, but he helps with the algae.