I have a SPD workflow with a lookup to assigned to groups. The workflow will send send an email to the group and assign tasks to the gorup etc. For some users (all site col admins, WF runs w/o problems). For normal contributors, the workflow shows stopped after entering a record.
Solution: This is permission related. The user has to be able to see the group memberships. Go to 'site settings' -> 'People and Groups', go to each group and go to Group Settings to switch the 'Who can view the membership of the group?' to Everyone. The workflow will start the next time you enter a record.