Make sure you have:
200 crew
600+ ox (crew needs 200 every 12 hours and they wont work if they do not have enough supplies)
600+ water
600+ food rations or other food commodity (make sure you have the right food rations, some did not work if i remember)
and reinforce alloys or hull segments or robotic hardware
then the base should start repair after a moment (60000HP every 20 seconds i think)