So I flirted with Knight via Confirmed Bachelor to get free repairs. However, upon reloading, I no longer get the free repairs and have no way to flirt with him again. This was a huge boon that's now entirely gone. I'm guessing there's no way for me to get this back.

It also appears I somehow lost my "Vilified" status with the Legion...

Alright - I restarted to figure out exactly where the problem lies. It does seem like it requires a reload to lose the Free Repair option. You can keep using Free Repair as long as you want provided you maintain a single game session. I'm not exactly sure where the bug is - if it's that you can use it more than once at all or if it's that it's not permanent (and should be).