Prevent Field From Updating On Follow Up Saves?
You can write a small custom module to lock down the original value of the field on edit, probably using hook_form_FORM_ID_alter would be the clearest way.

Difference between create new and edit node in form alter provides a decent example, try that. Basically, you have to check in the $form object for an existing node. If it's an edit form, you have a node id already; if it's a new node, you don't.