By some miracle it has and the damn workers are actually laying again!
To addresss the question you asked: How long do bees live? About 6-7 weeks? That is, of course, while brooding is taking place. Your bees survived the winter because they were not brooding. Now the workers they will dwindle steadily as the drone population increases and they cannot sustain themselves. Depends on how many bees there are and how much drone brood. Maybe a couple months, if they don't get robbed out.
The only way you are going to keep them going is to keep adding amounts (small, initially) of emerging brood; then some open brood, when enough bees in there to support them, then requeen when they eventually start to draw queen cells.
Like those above, I would certainly not be doing that and would have united at the first opportunity in the season.
In a normal season and perhaps with more than just the one good colony, worth a try for those that are determined not to lose a colony, but better for the other colony if you shift the hives together and then remove this hive after tipping out the bees on a warm day. Ha! - not even many of them at the moment!!
Then make a split later. Probably not a lot of honey this year, by the seems of things.
RAB