roboticus,
You may want to have a look at the Advanced Security add-in for Outlook. This allows you to tell Outlook to trust certain applications for certain activities permanently rather than being annoyed by the pop-ups. It doesn't sound like that is exactly what your problem is though. Read on for ideas on that.

First, you can run a service as any account you want - it doesn't have to be the system account. This means you can have the service running as the owner of the mailbox and that might solve your problems. If you are using Outlook as your client and Exchange as your server, you can also modify the permissions on the mailbox to allow another user to have full access without prompting for passwords. Of course, this all highly depends on your environment and local policies. None of this happens to help me solve my problem but it might help you with yours.