How are you accessing them from a laptop?
If it's using an email client (such as Outlook Express, Windows Live Mail or Thunderbird) and that client is configured to use the default POP3 settings, accessing mail from your laptop will automatically delete those messages from the server, making them unavailable to other devices (such as your tablets). If the default POP3 settings have been changed to 'Leave mail on server for 3 days' then accessing mail from your laptop will mark those messages for removal after 3 days (but they'll still appear on your laptop because copies will have been downloaded there). Indeed, that seems to be the most likely cause of the problem.
So you either need to change the POP3 settings on your laptop's email client to 'leave mail on server indefinitely' or, better, change the settings to use IMAP, rather than POP3, in the same way that your tablets already do.