When your unit has lost all of its hit points it will need to be repaired/healed to function again. If the unit isn't repaired/healed in a given time, the unit will cease to exist.
Remember to buy Elite units which cannot be fully destroyed, there is no given time to repair/heal these items.
Healing units costs Supplies and you can see the cost of repairing/healing by clicking on the wounded unit. Remember to ask your Allies for help to heal your units. This way you?ll be able to save a lot of Supplies.