Hey Matt,
I had the same problem with the AdMob Extension. The game builds then loads for like half a second, just enough to get a glimpse of the first screen, and then crashes. I couldn't get it to work, whatever I did.
In the end I stopped using the extension and just filled in all the necessary details for ads, in Settings->Mobile ( publisher key, certificate). I'm now using the built-in ad blocks for showing and hiding ads. That works just fine: game works and ads work.
Here's the link for the tutorial on Stencylpedia:
http://www.stencyl.com/help/view/android-ads/The ads might not show up immediately, but give it a few seconds, maybe a minute and they'll show up if all your details are correct. When you're testing the game, just be careful not to click the ads, so that you don't generate false clicks.
Good luck,
Andreea