Are you sure your ships are actually damaged? Ships might just fly below their maximum speed. This happens if they exit a system with a nebular, formation flight or some weird task group changes (and perhaps black holes, but I haven't found any yet, so I don't know).
You can check their 'current maximum speed' in the task group screen, in the upper left corner. It should show both an absolute maximum and a current maximum. The current one can be entered and set at your leisure, as long as it's below the absolute maximum (obviously).