Q:

How could an insectoid race survive despite a small gene pool?

Consider an insectoid race where each worker/soldier/role is bred as required by the queen. This is very similar to ants on earth. Periodically new Queens are born who then set out to found their own colonies.
We've discussed what happens when a starting population's gene pool is too small. However on earth colonies using this model clearly exist and thrive.
In a civilisation where every "minion" in a colony is bred from the queen (and presumably her own offspring) how does a colony survive past it's first few generations and avoid suffering from genetic issues caused by having a small gene pool or a single individual?

A:

Apparently the Gender of the Eggs hatching in a Insect Culture like f.E. Ants is determined by whether the eggs are fertilized or not. 
If the eggs are not fertilized by a male, they will produce a male.
If the eggs are fertilized by a male, they will produce a female.
This method has two main features interesting to your question:

Flushing out Degenerate Mutations Since the eggs hatch a male when they are not fertilized, and this egg represents the actual, unchanged gene pool, the male population that is suffering from the mutation will die, and the genetic mutation will not be reproduced by the Queen, since the male that would have to mate with her to transfer it is dead.
Relationships The workers of the Insect Colony can lay eggs that unfertilized will hatch male insects. But due to their relationship to the Queen, and the other workers (which are all sisters) it makes more sense to support the offspring of the Queen rather than have own one. 

When a Queen is mated with by a male the eggs receive half the genetic code of the male and half of the female, so there is recombination in each generation of females. That in combination with the above mentioned 'flushing' of the genetic makeup of a colony due to dieoff of sick male (which always represent the 'whole' genetic code of the colony) makes for is avoiding suffering from genetic issues after couple of generations.
Source:
http://en.wikipedia.org/wiki/Haplodiploidy

