Almost, teary-eyed/sniffles, twice. Both times it wasn't so much that I was going to loose the fish, it's that I was frustrated in myself and that I was powerless to do anything to help.
I had a juvi Queen Angel only for about 3 days before she developed a swim bladder infection. She couldn't keep herself down in the water and kept floating belly-up to the surface. I held her down in the palm of my hand for about 3 hours, she was so tired from the constant day before of battling the problem she wasn't even scared of my hand. She starting looking better after about an hour of resting in my hand (I wasn't holding her, more so 'cupping' her little body to keep it right up and lower in the tank), so I continued, but it was to no avail...She was so physically exhausted, just didn't have anything left...
The other time was having to put my Harlequin Tusk down. He was literally dying in front of me. I attribute it to organ failure from cyanide collection. He starting getting so bad his fins were rotting off when he tried to swim, and had nasty red sores, and he just laid virtually motionless on the bottom. I could tell he was in pain and he was past the point of no return.