That's a perfectly reasonable fear. There's always a risk of never waking up when using general anesthetic. Not a serious risk, but still a risk.

But I've been under lots of times (unfortunately) so it's a risk that doesn't scare me anymore. And my veins also suck. There's only one that's good and you have to cut off the blood flow to my arm for-frikken-ever in order to make it pop. And my blood pressure likes to drop in interesting ways when I get a needle put in. XD