This is a difficult one to call. It's always a hard decision to make but I try and make sure that I've done everything I can to help before making a final decision. Here's my list:
Make sure your water is as good as it can be. No ammonia, no nitrite and nitrates probably lower than about 40ppm. Make sure you're keeping up with your maintenance. Great water quality can go a long way to healing a sick fish.
Diagnosing the problem
Try and work out what is wrong with the fish. It sounds from your question like your fish has some kind of swim bladder issue because it cannot keep level. Sam A suggests using peas which can help to reduce the risk of bloat but I'm not sure will really help in this situation.
I've found that Melafix and Pimafix are great for a range of issues but this fish may be too far gone for this to help. Obviously, if you can its best to separate the fish and medicate a smaller tank so the others are not affected.
In my experience, tetras can be quite weak because they are bred heavily for their colours which might mean that other aspects of the fish are overlooked. If you've done all that you can and the fish is making no improvement, you may wish to make a decision. It sounds like you've got a good setup going though because you've not lost any other fish. This is an unfortunate part of the hobby.