Repairs can only happen if the engineer's main ship doesn't require repairs.
If the main ship is fully repaired the engineer will repair between 4% and 20% (depending on skill) of all escorting fighter's hull every 5-10 minutes.
Also when a mod is used to add engineers to stations, like w.evans does, fighters escorting tradeships are being repaired aswell.
Lemme know if you guys have any ideas for improvement.

Nexuslink: http://www.nexusmods.com/xrebirth/mods/505/?
Installation:
Download the file, extract the fighterrepair folder and move it to your extensions folder.
Deinstallation:
Simply remove the file, no savegame issues whatsoever.