No, of course not.
As long as you have an account with us, we will not delete any e-mails from you!
The only exception is the trash can, if you set it to this way, and only then.
Please note that some e-mail programs have settings for deleting e-mails above a certain size, number or age. Therefore, always check the settings of your client before you configure it to use your mailbox.org account or work directly in the mailbox.org web interface.