I do check on the repeatedly when I'm not asleep or at work. (At which times the game's set at half speed.) But despite the continuous attention and care, they still get sick a whole lot more then I think they should.
I've got all 7 magic fish now anyway. I'm thinking of putting it on the "stop" and not play anymore. Though I still have 200 breeds to go to find them all. It's getting a little bit boring. I wish after you got all the upgrades and all 7 fish there was some little extra thing to do. Like create an 8th magical fish or even having to fight your way to a place to release offspring of the magic fish to restore the balance all while trying to fight bad guys who want to kill the fish. Just something a little more exciting then breeding, selling, and curing fish continuously.
But at least Fish Tycoon kill time till Plant Tycoon's avalible for windows.