I'm the same way. I spend a good amount of my time being pulled into production issues or debugging a particularly difficult issue with the product. In both of those cases, the "code" changes often take only a few minutes, the problem solving can take hours.

I get a lot of satisfaction from that. Of course that means that as a team lead/manager, I have to have a lot of self discipline to allow my team members to do the same and not try to solve every problem.