You can check out as many towels as you want and as often as you want - just make sure you return as many as you checked out before the end of the cruise. There also should be special towels for the ports in your room. I don't think I ever had to go to the pool area to get any towels to take ashore. I never pay any attention to thinks like that, thats why I bring Esther along.
It's a good thing she doesn't read by posts 
Sonny