I don't know the timer, but at some point, they put a DoT on you that deals rather heavy damage. They will immediately re-apply the DoT if you engage them before they get their health back to 100%. All the Minions/Champions that you managed to kill will not respawn, however, so just wait a little untill they have full health and try again and the DoT thing is gone.
Oh, if you remain dead and watch them regenerate, they will regenerate it back rather slowly. Just resurrect, wait like 10 seconds, then try again and they usually have full health again.
As a tank Barb in late Act 3 I have repeatedly hit enrages and survived for well over 30 seconds. The enrage builds up over time, starting with a (very) small DoT and building upwards. If you're dying from the first two seconds then you are playing incorrectly.
My favourite encounter in that regard is the Last Stand event in the Kitefest Wo...err....Festering Woods. Once the skeleton pack - which is naturally fast already - spawns with fast horde shielding mortar you are going to hit enrage unless your gear completely allows you to obliterate them on spot. I am now in the position of killing them before enrage with moderate amount of challenge unless invulminions is up. If enrage is up then there is a time when you are exposed to a dot however even with my 32k health it would take more than 2s to kill me and enrage is on timer as well so there is a time after enrage where you can still kill the pack. However it seems monster stats go up by a bit after enrage has passed (my observation).
WoW: Crowcloak (Druid) & Neesheya (Paladin) @ Sylvanas EU (/ˈkaZHo͞oəl/) | GW2: Siqqa (Asura Engineer) @ Piken Square EU
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Not really hard, go to town and port back when you reach enrage, if your in a group all party members needs to port to town then go back, if ur doing it fast enough, the hp wont reset but the "enrage" will, cake.
Enrage is a bullshit mechanic that shouldn't exist in the game. You shouldn't be penalised for taking 10 or so mins to down a very very hard elite pack. It's rubbish, this isn't a WoW raid.
^This
I've had to deal with enraged elites before (fucking fast/shielding of those goddamn wasps in act2, IN INFERNO ACT2, ELITE PACK KITES YOU FOR 10 MINUTES) and it just slowly drained my health, I could outheal it for about 20 seconds before I died. But that's because I have like 74% armor reduction and another 70% resist all.