I think there are two possibilities. 1) you aren't securing it well enough at the front end and it is working free and unwinding. 2) If it is a fragile tinsel, the fish are simply chewing through it and leaving it ragged.
When tying patterns you plan to actually use , I personally think tinsel sucks for ribbing. Unless you reaf down on the stuff while winding and secure it with multiple thread wraps, it will eventual come loose... unless you're not catching fish. The tinsel stays in place quite fine if the fish are ignoring the pattern.
Since I gave up on tinsel and switched to wire, I haven't noticed ANY drop in a catch rate of a pattern where I've substituted wire for tinsel ribbing. And the wire stays put no matter how many times a fish-type unit chews on the fly.
Try to double the tinsel back when you tie it off in the front. In other words take a couple of turns of thread with the tinsel pointing forward, then turn the tinsel to the back of the hook and take a couple more turns of thread. That way it is locked in place. Oval tinsel is best, mylat flat tinsel can shred when hit by a fish tooth and come loose.
I'm with Gene on using wire whenever you can get away with it. Tinsel can provide a broad segmented look better than wire, but that isn't often necessary.
There's some good French oval tinsel that is pretty tough, as Bob mentions, but even it is not as strong as wire.
+1 on the wire. I've also found that ensuring you are wrapping enough tinsel onto the hook to ensure its secure helps. I see a lot of SBS's that show them tying in the very tip only. I always think to myself....that won't last.
If you are using mylar tinsel it doesn't stand up to fish teeth. You can use the real stuff - Lagartuns French Tinsel (tin) - or, as others have suggested, wire. A med silver wire would probably do the trick. I sometimes even wrap a fine wire over the tinsel. Suggestions based on the assumption you are tying in the tinsel properly.