Problems all drawing tablets can have
They lose or damage their pen. Replacement pens are expensive - it may cost a significant portion of what you paid for the tablet.
The pen no longer reports pressure
The pen pressure is stuck at 100%.
The tablet driver cannot detect the pen.
Problems unique to pen displays
The pen display doesn't show anything.
I have put together a list of troubleshooting articles to help with these problems and many others. More here troubleshooting