Can you log into your account on runkeeper.com but not in the app? Yeah, this one's strange.
If you want to stay updated on a fix submit a ticket and please answer the following questions so we can investigate further! Be sure to put "Android: Can't Log In" in the subject line.
1. What is the version of Runkeeper you're using?
2. Did you logout of the app yourself, or did the app log out out automatically?
3. Did you originally create your account with the Google option, or did you sign up with your email and create a password?
4. When did you first run into the problem?