None of the butyl mats like Dynamat Xtreme will go bad. Asphalt will, as the volatile compounds that keep it flexible evaporate over time. Butyl stays flexible and actually forms a stronger bond over time.
If you are asking about it going bad because what you have installed doesn't seem to be as effective as it used to be, there are a few possibilities. If it's asphalt, what I said before. If it's butyl, you could have installed it onto a greasy surface, in which case it might not be in contact with the sheet metal anymore.
For any of this stuff to work, it has to make really tight contact with the substrate. Clean surface and no air bubbles under it. What's most likely is that you have just gotten used to the level of sound deadening you achieved and want more - just like everything else that's good //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif
You can pretty much tell if you have reached the point of diminishing returns by tapping on the sheet metal. If it rings at all, you can use more. If it makes a dull thud, you'd be wasting your time. Assuming you have enough vibration damper (like Dyna-X) installed, there is still a lot you can do. The next most effective step is covering the areas you have already treated with 1/8" - 1/4" closed cell foam like Ensolite or Neoprene. In my experience, this makes a huge difference, adds very little weight and is not too expensive. If you want a quiet car, and/or a sound system that sounds its best, this is a critical step. I've got it everywhere - inside my doors, lining the tunk, under the carpet, above the headliner and behind all trim panels to keep them from rattling.