I think if you're dead, you'd log out. I don't ever or rarelyt log out as such, but I don't show up as online and logged in unless I actually have the forum open. Also, it takes about 15 minutes I think for it to register you as logged out.
Unless there is a specific reason to delete an account, members stay members. We have some prominent members who show up at rare intervals and it's good to see them. We often have members who are gone for months then come back, so 3 months would not be reasonable, that's for sure. IDK if there is an actual cutoff date for keeping an account open, but maybe dv8 or Steve or Hoogle would know.