Pretty much infallible I guess yeah. I was however entertaining this idea a few weeks back though. I love GPS and who doesn't, it's great for going for a random ramble and finding your way back even if you don't know the area. Fantastic for leaving waypoints of potential BOL to come back and investigate later, or even places of natural food supply, streams and rivers for water, and even where you have left caches. But you might want to back that up with details on a physical map because if you do have trouble you need to know where things are, if you can't remember fully then you're screwed.
The only things I could come up with that would be bad, apart from actual device failure, would be a Coronal mass ejection from the sun, which I guess could have the potential to knock out satellites if strong enough. No doubt we would be well informed about the possibility of an event like this before it happened though. Then the possibility that whoever is in control of the satellites can just simply shut them down and deny anyone using them.
The other event I thought about would be the same as you stated, the possibility of something happening at ground control and it being left unmanned or without power. After some research I found someone stating that according to the book in this link, they reckon that a satellite would probably go out of commission after about two weeks without intervention from ground control. I imagine they are constantly tweaking it's orbit path, synching time and position, uploading updates and such like, and without that it seems they would be useless fairly quickly.
Link to the book that some guy pointed to that had this research in ...
http://books.google.co.uk/books?pg=PA21 ... edir_esc=y