Destiny Nightfall with 2 players, one dead, did we time out or did I run too far away?

Solution 1:

From experience if some of the party are in a darkness zone and some are not, if the people in the darkness zone die it counts as a wipe. In a normal instance this means everybody respawns at the start of the darkness zone - an interesting experience if in a strike and some people are running ahead past all the optional encounters and die in the darkness zone those hanging behind in the optional encounters get teleported up.

In a nightfall strike of course this would mean it counts as a party wipe and thus boots you back to orbit.

So the answer to point 1 is no, it doesn't matter how long your partner has been dead. The answer is point 2 pretty much - you ran far enough away to be out of the darkness zone. 3 is pretty much Not applicable therefore. :)