Can I force password protection of specific apps on the iPad?
That's not a general feature of iOS. You can lock the entire device, but not certain applications. 

The iPad mail app does not have this as a specific feature either - when adding an account you must store the password so it can check for new mail in the background.

There are some third party apps for iPad that require a password to access them but I'm not aware of an email app with this feature. But it might be worth a search.