Actually I just came here seeking help for the same problem. I also have a mini that was a christmas gift last year - A week or so ago it was working fine all morning, then suddenly the click wheel wasn't working. At first I just figured i had the hold button clicked over - that wasn't it. The part I found oddest was that all of the other buttons still worked. (Menu, Play, The center button and the skip track buttons). If I turn hold on and then turn hold back off the click wheel will work for anywhere between 5 and 10 seconds then stop again. Same with pressing the center button or the menu button - it will let me scroll with the click wheel for a few seconds then stop (and I have to press other buttons to get it to work again).
In other words I can skip around after a fashion but it's very annoying and more importantly I'm concerned that there could be a more serious problem in the future. [I have reset it, upgraded to most recent software, etc, and nothing has worked so my assumption is that it has to be something more along the lines of mechanical/hardware]
Windows XP