It had been mentioned on the forums before, and I had written this for my personal use. It is a small mod that just adds a ship repair facility to starbases, increasing ship repair rates for ships in the starbase's area of effect. There are two starbase modules, one which unlocks with Zero Gravity Construction and the other with Large Scale Construction. The first module adds +3 to the existing repair rate. The second module doubles the existing repair rate. This can be easily edited to suit your fancy.
Download and Install
Download the mod here: http://www.mediafire.com/download/z9lhdkn839rhigl/ShipRepair_-_Starbase_Module.zip
Unzip and place the folder "ShipRepair - Starbase Module" in your Mod folder (usually Documents/My Games/GalCiv3/Mods)
Make sure mods are enabled in your game options.
(Thanks for those who provided feedback to make this work.)