I had this problem last night. Took 6 hours to fix rep. An evening I could have used to further progress in the game, which I didn't.
I see 3 ways to fix this.
1. As someone said up above a permanent license.
2. A checkbox that "auto-renews."
3. Have AI captains STOP salvaging and either recall or set to defend all fighter salvagers when a license expires.
Perhaps, optionally, a checkbox when ordering an AI to salvage that OVERRIDES the above listed license behavior, in case you don't care if the rep drops. This would be mutually exclusive with auto-renew, obviously.