You should get a new piece of tubing. It is now most likely too short (actually most shop install them too short to begin with). Also it is old and could easily fail.

It should be long enough so that it barely stretches at full draw -- just enough tension to keep your peep straight. It should not stretch where it were to part it could snap back and hit you in the eye. By keeping it long enought to just turn the peep you do not have to worry about a failure or an injury to your eye.