Princesses come in two flavors, or stocks. Pristine Stock bees will never die off, Ignoble Stock bees will eventually die off, and if you genetically modify them, might not survive the process. It is suggested getting a bunch of different bees, preferably of pristine stock, before starting to breed. You might find it advantageous to run some of the wild bees for a short period in order to build up Drones.
If a bee is Ignoble it means that the specific Princess will die and disappear after a random number of breeding cycles. Specifically, after about 100 breeding cycles, there is a 2% chance per cycle that the Queen will not produce a Princess among her offspring. However, if the bee is Pristine, it will never die out and you will be able to keep breeding the bee.
Use Ignoble Princesses in Bee Houses to get your initial honeycombs. Go ahead and use Ignoble Princesses to breed the first couple tiers of bees, and if you're ever worried about one, just Portable Analyzer it and check how long it's been alive. If you need to, retire her to a Bee House.
Ignoble queens have a tiny chance of not producing a princess in an Apiary after being bred for 100 +- 20 generations.This chance is small, but it is there. Therefore, it might be for the best to not breed the Ignobles and just use them for getting products in a Bee House, as they will always produce a princess in a Bee House.
Ignoble - This specific Princess will die and disappear after a random number of breeding cycles.
Pristine - This specific Princess will never disappear.
Long story short - if you get an Ignoble Princess - you should make as many Drones from that Princess - and then use those Drones to turn a Pristine Princess into that type.
Drones do not carry the Ignoble/Pristine trait.
Rocky Princesses are good bases to turn into other types because as far as I can tell - Rocky Princesses are ALWAYS Pristine.
Later versions of Extra Bees changed the Rocky Princess to have the same Ignoble chance as other hive bees.