that is correct.
if gladiator is dead - it only resurrects.
if gladiator has injuries - it only heals them
time runs out to 0 and gladiators are only partially replenished. If you refresh the page, the timer starts all over again and then you're healed, so it appears it takes twice as much time.
However if you stay on the same page, it works as intended.
I've tested on newest version of Firefox.