Insulin pens can be faulty, there was a post here recently about someone having a broken one and one of mine broke recently too (well, I'm not 100% sure it broke, it might have been user error on my part, but I've asked for a replacement just in case), so I imagine Byetta pens are similar so can also break.
Are you using disposable or refillable pens? From your post it looks like disposable ones, did the two faulty ones come from the same batch/box? If so, if I were you, I'd leave the rest of that box and start a new one, just in case. Also, if you don't already, make sure you always have a spare signed prescription from your GP so you can get more pens if anything happens again.