I stopped using Sparrow due to a bug in their implementation of two-factor authentication for Gmail (it would always "forget" my app-specific password on startup). I got at least one (unhelpful) response to my support request(s) but the trail eventually went dead, with no resolution to the problem.
I'm not sure if it matters, but are you using a "regular" Gmail account or Google Apps for Your Domain? I'm doing the latter and still can't get it to stick (tried again this morning before posting). When I quit and restart Sparrow it cannot connect, and I have to reset the password before it will fetch my mail. Oh well!
