Sounds like a relay or breaker is getting hot and failing, then cools off and works again for awhile.
I could not find any diagrams specific to your year/model, but I do have a couple in my files (maybe its the same or close).
On the front bay, there are circuit breakers for the AC fan and other AC components. You should see if power is going through the breaker at the time when dash fan quites. Just test with a 12V test light and see if the output side of breaker has power.
I found two electrical diagrams (2008) dealing with Dash AC. Maybe something there will help.
Good luck.