The food 'fuzz' is a clue - that suggests colonisation by bacteria or fungus that aren't part of the nitrogen cycle, so although your water tests OK, I suspect your biofilter is only just coping. You may also have elevated phosphate (you can buy a test for that) which can stress fish. Bacteria is always present in your tank (and everywhere else) - your fish only succumb to it if they are stressed or physically damaged and weakened, so you will have to do your best to work out what what caused the problem. If it isn't phosphate or ammonia etc., then you have some other sort of contaminant, so I'd be inclined to give your tank a good clean (hoover the gravel etc) and do one big water change (80%) if you haven't done that already, then change 25% / week from now.
p.s. I don't know about the water in your area, but if it is treated you will need to declorinate / age it before you use it.