It sounds like your workflow is triggered when an e-mail is received.
If it only works when Outlook is open, then you need to review the E-mail access type - incoming on your CRM user record - it is almost certainly set to: Microsoft Dynamics CRM for Outlook. This means that incoming e-mails destined to be stored in CRM will be processed by the CRM Client for Outlook. If your Outlook isn't running then this can't happen.
To allow e-mails to arrive in CRM regardless of whether your Outlook is open you need to use the CRM E-mail Router and change the E-mail access type - incoming on your (and other) user account to Forward Mailbox (you could use E-mail Router but I don't recommend that).
I suggest you review this document:
http://www.microsoft.com/downloads/details.aspx?displaylang=en&FamilyID=8ea05b4e-825a-4db1-ad59-d894aa5ef33ePlease post back if you need further help.