None of my ships are repairing??!!??

[Suicide Junkie]

Try moving all but one of the ships away, so it is the only one that can be repaired.
Also watch out for damaged bases and stuff in the sector that may be taking up your repair points.

[PvK]

If you're playing using Proportions Mod 2.x (?), and have upgraded your game from an earlier Version of Proportions Mod, some components may not be repairable, so you'd need to refit to a design that uses current components.

Also, even in unmodded, there are a few component types which intentionally can't be repaired with a mere repair component - they require a full shipyard. They are the emergency components and stellar manipulations, mainly.

PvK

[Alneyan]

The Stellar components can be repaired everywhere (a common design for such ships is with a small repair bay to allow them to repair themselves). The Emergency components (Propulsion and Supplies) do require a spaceyard, as any modded component with these abilities.