Death

When the health of one of your knights reaches zero, they will be defeated and become incapacitated until their health recovers. Once their health moves above zero, you are free to use them again, but obviously your knights will not last long in combat under these circumstances.

If they are defeated in the Arena, their reduced health does not carry over into the main game and in fact you are able to play another match in the Arena straight away, if you have the Energy for it.

If your knights are defeated in the single player quests then that's it, you have to sit out and wait for their health to recharge. However, as long as you don't start a quest in a different area of the game world, or on a different difficulty level in the same area, you are able to resume from the particular stage you were at before they were defeated. So, for example, if your knights were wiped out at level 3 of the Epic Stage of Relic Ruins (for some reason), then you would have to wait for them to recover some health, but would be able to resume at level 3 again.

If you pay gems, you can continue instantly. Note that if you want to select different knights to take part, or spend some time battling on another area of the map, you have to forfeit your stored progress - you can only be questing in one place at a time, basically.