Am I correct that units never regain HP?
I tried placing damaged units on a base, but they did not gain any.
Correct. There isn’t such a feature at the moment. I’ll put it on ideas list.
I can think of a few options that could be implemented:
- +1 HP/turn gain while on your own base.
- +2 HP but costs something, maybe 10 coins?
The options introduce a dilemma. Do damaged units stay and fight and die or retreat for a benefit later?
Since you would not use your forward bases for repair, the units would have to travel to the rear.
If one does repair at a forward base it prevents new production there.
If you do decide to add this, I suggest the HP gain is done at the start the turn, giving the opponent the chance to destroy it on their turn.
Related ideas:
- Medic unit (Jan has made graphics for those with the rest years ago so that’s ready).
- Special repair/healing base, or separate repair/healing bases depending on the type of the unit (but this would require creating the graphics).
- If ordinary bases are adding hp then units could be acquired with 10 hp and left to rest there to boost their hp up to, say, 12.
I’m not so keen on the medic unit, as it defeats the requirement of unit withdrawal to repair. Unless it only repairs infantry and slowly +1HP. Then you could still require armour to repair at a base or repairbase.
I really like repair base concept. This would limit the repairs to only a few locations rather than all the bases, much better for strategy. As for the Icon, you could just modify the base to replace the sat with a cross 
at least until an artist can do it justice.
Another option would be for normal base to repair at +1 HP and repairbase at +2 or +3 HP
Of the suggestions I vote for the repairbase only +1HP 10c cost or +2hp and 20c.
The cost thing is interesting, infantry effectively cost more to repair than build, 1c per HP but build @ .75c per HP, while tanks cost 2.5c per HP, so one has very good reason to repair tanks. Makes for really interesting decisions.