First of all, it helps to know what type of monitor it is, as certain monitors have certain common failures that cause these types of problems.
It sounds like a hold problem. If the caps are starting to dry out and fall out of tolerance, the picture will sometimes roll (go squiggly) randomly, or lock into position off center. A cap kit will usually fix this, but you can't really write it in stone until you've had a chance to see it in person and do your own investigating....