In my current game I've been training veteran companies of archers.  After the first battle they usually get a level or two which is fine, except when a unit gains a level and has taken even 1 damage their current health doesn't increase. 

This means a unit that starts with 200/200 health, gets hit for 1 and ends the battle at 199/200 then gains levels can end up with something like 199/500.  This also means on the next turn instead of 12 guys being in the company it reduces to something like 5 guys instead.  This is a huge reduction to the combat effectiveness of this unit for many turns after since healing takes so long.  All because the unit took 1 damage.

A similar scenario occurs when a unit enters a city.  A company of 12 can be reduced to 5 or less guys.  It also works in reverse.  A unit which is defending a city a takes damage can walk out of a city and be at 100% health because the max is reduced to below the current hp.

I don't think it's good that I spend ~20 turns training a company, get one battle out of them and then have to let them "heal" for another 20+ turns just so they can be at full capacity.

This could be solved easily by having unit HP remain at a percentage when leveling/entering a city instead of a fixed number.