Tetra troubles

I've had my aquarium for 4 years and had several fish die, but my Glo-Light
tetra seems to be dying and I'm not sure why. He's been in my tank for 2
years and has never demonstrated any signs of illness, but I found him at
the bottom of my tank desperately trying to swim around, but still stuck at
the bottom. If I try to push him a little bit with a small net, he can get
off the gravel, but then falls back down again. I have a 6 gallon Eclipse
System 6 with a heater, carbon filter cartridge, and a Bio-Wheel. I've
gotten the fish into a hospital "bucket" with fresh water, dechlorinated,
and a small supply of food. I'm debating whether or not to use a
tetracycline tablet, which is a wide-spectrum antibiotic that has worked in
the past. Help would be appreciated.