myBalsamiq has a "Remember me" checkbox on the login screen. If you've checked it myBalsamiq shouldn't ask you to re-login, unless the server has been updated.
If you get repeatedly asked to log in after an unusually short period of time, there may be a problem with old myBalsamiq cookies hanging around in your browser, and you may have to clear your cookies. For instance, if you've checked "Remember me" and you're asked to login more than once on the same day, then it's probably a cookie issue.
To fix this, delete your cookie for *.mybalsamiq.com and log in. If clearing cookies doesn't help, let us know and we'll help figure out what might be going wrong.