I'm managing a small team of developers. Every so often we decide we're going to spend a day or two to clean up our code.

Would it be a good idea to schedule regular time, say 1 week every 2 months, to just cleaning up our codebase?

No.

Fix it while you're working on it:


If you wait to refactor the bit you're working on, you'll forget a lot about it, and have to spend time to get familiar with it again. 
You won't end up "gold-plating" code that ends up never being used because requirements changed

