The mailbox store limit in Exchange 2003 standard edition was 16 GB. They bumped this up to 75 GB with the recent release of Service Pack 2 for Exchange 2003. If your store is too big, you can see this problem where the store will mount for awhile then dismount. You can see where the logs are stored in system manager by going to Properties on the “First Storage Group.” The transaction log is listed there and is typically, %DriveLetter%Program FilesExchsrvrmdbdata. The store location is found by going to Properties on the store that is dismounting, then clicking on the Database tab. If either hard drive is out of space (assuming the logs and store are on separate drives – a recommended practice) you can have this problem. If you are doing a backup, the logs are supposed to remove themselves, if not, you have to delete them periodically.
Hope this helps.