Motorola RAZR V3c
Help my razor has a clock problem
1) It's a network issue.
2) You got a bad phone and it might need to be replaced. Hopefully it is still under warranty.
What software version are you running? I kind of vaguely recall some people had problems with the alarm function until they got their phone flashed. I don't know if this affects the clock issue but the alarm clock was a known bug.
My suggestion would be to call VZW or take it to a store and see what they say. Sorry I cannot be more helpful. These are just my ideas, I'm no phone expert.