First of all, what is absconding?
When a colony absconds, all of the bees leave, including the queen. This is rarely a spur of the moment decision by the colony, but is weeks in the making. Once the decision is made to abscond, the foragers stop bringing in nectar and pollen for storage, the queen stops laying, and the colony waits around for the pupating bees to emerge. Then the workers engorge with honey and off they go in search of a new home. What the beekeeper finds is an empty hive.
The triggers for absconding are not well understood or agreed upon, but some things are considered valid.
#1 - something in the hive has them disturbed and they believe they will not survive in that environment. This could be a certain odor; a high incidence of disease; a high rate of pests like Varroa, Small Hive Beetles or Wax Moths; continuous disturbance by outside forces (like skunks scratching on their doorstep every night; close proximity to a manufacturing facility that emits a disturbing frequency; or a beekeeper opening the hive every other day.).
#2 - lack of resources. A hive that's in full sun all day and there's not enough water available to cool the hive sufficiently is a bad environment. Resources (nectar and pollen) in scarce supply is also a bad environment, they need to find a place that has a sufficient amount of both.
#3 - inadequate ventilation, which adds to the summer cooling problem and the winter air exchange.
If a colony absconds in spring or early summer they have a pretty good chance of surviving the coming winter, same as a swarm does. The colony will live in a temporary area for a period of time until scouts have located an acceptable nest site.
When a colony absconds, all of the bees leave. They aren't reproducing, they're trying to escape a bad situation. This isn't unusual behavior, and in other parts of the world honey bees actually migrate, particularly in the tropical zone. In some places it's an annual event with the colonies leaving for better forage sites when resources get low, with the same colonies returning to the same nests they left when forage is again available. Some researchers think that honey bees in our temperate zone may also migrate for better forage sites, but the phenomena is pretty much identical to absconding so it's hard to prove.
If a colony absconds, and I've experienced that several times, the hive should be checked to see if anything can be determined as to what triggered it. An impossible task in my experience. Some people use a propane torch to sanitize the woodenware, some burn the hive. I tried torching and the boxes smelled like a cold campfire afterward so I didn't do it again. Instead I mix about 1/2 teaspoon of tea tree oil with water and a pinch of lecithin in a pint spray bottle and spray everything down making sure to get the liquid inside of the cells and running down the insides of the boxes. Then I let it dry and put bees in when I have a colony needing a home. It works. (Tea tree oil is antifungal, antibacterial, and the bees like it. Smells like Pine-Sol.)
If you're able to capture an absconded colony, don't return it to the same hive. I did that once before I knew anything about absconding, and the next morning they took off and didn't even bother to stop to hang out nearby (I had gone to check on them just as they took off.). They had had enough. But the probability is good that they would have accepted a different hive in a different location.
As long as we have our hives well sited, in a location with sufficient resources (nectar, pollen, propolis and water) and few disturbances, the bees should stick around. If they do abscond we may never know why, it's just another thing that bees do.
-Gerard