Mail app keep going offline

Hello,

I haven't been able to find an answer that works for my mail app. I'm using the OS X 10.4. My computer is shared so I'm often logging into my side during the day. I've had this ongoing problem where all 4 mail accounts I use go offline and they stay offline for days. Then eventually it all starts working again. I've tried connection doctor and the top part show a green button and then next to each account it shows a red button that says something to the effect of checking to see if my accounts allow SSL. All the accounts have the SSL option checked. When I select view details in the connection doctor box nothing shows up. I've tried a restart and keep trying to hit take accounts online to no avail. Even tried to edit the SMTP option in the preferences mail accounts setting.

It's driving me nuts because it happens often and I can't use mail during he time. Any ideas?