If my shield (or my hazard protection) fails and my body takes damage, I can get health from all sorts of things: wall dispensers, shiny artifacts, plants, helpful aliens, etc.
What about when my ship's shields fail and it takes damage? How can I heal that? (My current ship started out with 5 or 6 little ship icons below its shield bar; now it has only 2.)
Quitting the game and starting up again seems to have done the trick. My ship was back to 6 little health icons when I did that.
Note: In this case my game actually crashed (because PS4), so I'm only assuming that quitting the game would have had the same effect. (The save point that reloaded was from a couple minutes before the game crash, which was several hours after my ship was damaged.)
At the very least, you can talk to the NPC in a space station, and providing you have the appropriate rank with them you can ask them for repairs, which should repair your ship.
I've noticed when docked at a planet based trade station (a multi platformed one) that when I went back to my ship the damage was repaired. Earlier in the same play session I'd stopped at a space station in hopes of recovering ship health and it didn't happen. I don't often get into ship combat, and when I do I usually die, so this is the only instance of ship repair I can account for. Not sure if this was the actual cause for repair or if traveling a good distance (shields maxed, like how your health recovers) had played a factor into it, but I'm pretty sure it only happened after visiting the planet trade station. If you encounter a similar experience I'd love to know. Hope this helps.
Park in a space station and let it autosave. Then restore current saved game and your ship health will be full.
Aside from the answers given by the other answerers, warping also seems to repair ship health damage, which is fine if you aren't interested in exploring that system.
