If you are careful, dont overcrowd or under clean, and are lucky, you wont encounter disease problems with the fry. If you do have disease problems, then you have a tough row to hoe: most medications that will effectively treat the likely diseases (parasitic infestations) are also fatal to the fry.
I was not lucky, even though I did daily cleanings and water changes. Up until about 6 weeks I lost virtually no fry; literally maybe 2 or 3 fry out of several thousand. But then things fell apart.
What I saw was that fish began to develop swollen gills and, in more advanced cases, whitish protrusions from under the gill covers. I asked a lot of people about what this might be. A number suggested gill flukes. In retrospect I believe it might have been Oodinium or Ich, both of which are parasites that do infest gills. On adult fish the infections would have been obvious on the fishes bodies, but the fry were still pretty small.
I tried a bunch of things: mild Formalite I treatments, salt, and potassium permanganate. It appeared that the potassium permanganate may have helped a bit and was not as hard on the fry as I had expected it to be. But basically for weeks I was losing 50 fry per day. Even with thousands of fish, you cant sustain this kind of loss rate for long. This was a real low point for me.
What I ultimately ended up doing was catching out the obviously sick fish and disposing of them. The fish that had reached an inch in length seemed to be able to get ahead of whatever the problem was, and were unaffected. So basically the fry either outgrew the problem or got sick and were disposed of. I should mention that I had a number of different tanks at this point, and not all the tanks were similarly affected. But I did have losses in all of them. The 55-gallon tank that had the natural spawning was the first hit and ultimately hardest hit. I ended up carefully sorting through all those fish and sterilizing the tank.
As a sort of epilog, at 5 months I had quite a number of fish with short gill covers and stunted growth. I do not know if this was genetic or environmental, but my suspicion is that the earlier gill infections left some fish with distorted development of their gill opercula. I sorted out all these fish and disposed of them (if you are wondering, "dispose" is a euphemism for freeze and compost). There were probably about 100 of these fish. I am still left with the question: did the disease cause shortened (deformed) opercula or did genetically shortened opercula make some fish more susceptible to infection. I believe the former.