Thanks for a great question. I'd be happy to point out what's most probably happening here.
You can indeed use custom data fields as triggers in an automated workflow, but I think what might be happening here is that your "service date" field's data type is not a date. This would mean that Emma doesn't read that date as a date, but rather as text.
Without knowing which specific account you're working in it's hard to be more specific than that. You can check the type of data for that custom field from the "Manage contact fields" button on the Audience page. If this is something that you need to change, you'll want to create a new field, export your contact list and reimport it mapping your new "service date" field.
Rest assured this won't do anything to your contacts other than adjust the mapping of that particular data field. This will only take a few minutes.
You will then see that field as an option for a date-based trigger!
I hope that helps, please let me know if you have any follow-up questions on this though :)