I used to struggle when the time came to end the suffering of a dieing fish. I just remember that in the wild there would be a larger fish to come along and end their suffering. By euthanizing them when they are severely ill with no hope of recovery, you are helping to mimic the natural environment by removing the sick or old. I still wait quite a while before euthanizing and try to make myself think that they are improving when they are not.
What is harder for me is to see the reaction of their mates. When I had to put down my female Florida Flag Fish, the male didn't eat for three days and just circled the tank looking for her.