Livebearers give birth to premature fry for a variety of reasons. The most common is stress. I found this recently with a very pregnant wrestling halfbeak who I moved to a breeding tank just a bit too late. She gave birth to fry that were able to wriggle about, but they couldn't swim properly and their yolk sacs were still present. They were all dead within two days.
So, avoid stress. Never, EVER put a large female livebearer (molly, swordtail, or halfbeak) in a breeding trap or breeding net. That's an invitation for miscarriages, because the female is apt to feel confined, thrash about trying to escape, and then miscarry. Avoid moving pregnant females from one tank to another, and certainly never net them. If you need to move her, carry her in a cup of water so she is constantly supported.
Another big factor is diet. Livebearers, just like human mothers-to-be, need a good diet. Trace minerals and vitamins are probably very important. Pregnant livebearers should be getting at the very least the best quality flake food you can buy, which in most cases should be algae-rich "livebearer flake" rather than generic tropical fish flake. I'd also consider using frozen or live supplements like bloodworms and daphnia. In the case of herbivores like mollies and platies, providing some algae in their tank for nibbling on is probably useful, too.
Environmental conditions are obviously important. Mollies, for example, like warm water, warmer water than most other tropicals. Raise the temperature of the breeding tank to 26-28 C (79-82 F), but be sure and accommodate the lower oxygen concentration in the warmer water, either by adding more water movement (e.g. and airstone) or simply ensuring the tank isn't overstocked. Mollies like brackish water, so adding some salt is helpful. Conversely, many halfbeaks like soft water, so using rainwater to lower the hardness and pH seems to help them. Basically, read up what the fish likes best of all, and provide it.
There's a big difference between rescuing the odd baby platy from a community tank and actually seriously breeding livebearers. The hobby, for whatever reason, tends to think livebearers are "boring", "just-add-water" kind of fish, but that's actually not very accurate. While livebearers are certainly easier to breed than, say, tetras, there are plenty of challenges and things to look out for. This becomes especially true when keeping somewhat temperamental species like sailfin mollies and Celebes halfbeaks, and even more so once you get into the really unusual stuff like pike livebearers and four-eyed fish, let alone stingrays!
Cheers,
Neale
