AFAIK MilSB are able to repair ships but the current game doesn't offer such a module.
What's standardly considered as SB repair is +20 hitpoints, but this can only happen when that starbase is damaged.
Constructors don't disappear into nothingness. If no module is availabe then you'll get a prompt about it, and the constructor will wait before the starbase.
You could always try to select your modules manually, it's IMO the better way and you know for what your constructor did disappear for.