Galaxy Nexus with Jelly Bean automatic shutdowns and signal problems.

So I've had my Galaxy Nexus for about three months now, and lately I've been having a lot of trouble with automatic shutdowns and some signal problems. I think the shutdowns may have something to do with the battery shifting positions slightly because they frequently happen when the phone is jolted somehow (such as me hitting the back of the phone or laying it down none too gently). This may sound stupid, but it's really, really annoying when it happens, and it doesn't take a concentrated effort to make it shut off. Sometimes, I'll get the phone out of my pocket to find that it's off. I just have to turn it back on regularly, without the need of removing the battery, but it still worries me. Even more worrisome though is how it has two times in the past few weeks refused to cut back on immediately. One time, it wouldn't come on for around 20 minutes. On top of all of this, my phone frequently can't find any network signal at all in places where other phones, including my old iPhone 4, can still get service. It's annoying. Sometimes I can go to settings and search a network then register to it, but that's time consuming and it doesn't even work all the time. Basically, I'm just wondering if anyone else has experienced these issues with their Galaxy Nexus and what I should do about them. Thanks!