A collection of posts by David Weber containing background information for his stories, collected and generously made available Joe Buckley.
Actually, that's a better description of what happens in the Starfire universe, where the treatments actually do "slow down" the bio-clock. In that universe, pregnancy, surgery, wound recovery, etc., are usually accompanied by the use of drugs which temporarily "shut off" the slowing down… or else pregnancy would last for something on the order of 27 months and everyone would be busy tubing their children!
In HH's universe, the cellular changes which accompany/cause the aging process are shut down for a couple of centuries. The factors within the genetic code which cause an organism's cells to "forget" how to reproduce themselves perfectly are neutralized, but all other physiological processes continue at their normal rates.
What happens at the end of the prolong process is that the neutralization of cellular amnesia wears off and the individual begins aging--at what we would consider a normal rate--from the point at which the original aging process had been arrested. Thus someone frozen in his/her mid-twenties would probably live at least another 60+ years (given the other medical advances available to them) from the time his/her generation of prolong wore off.
This does not mean, however, that everyone will continue to look all new, shiny, and unwrinkled just because of prolong. Stress, deprivation, extended periods of intense worry or exertion…. Any number of things can cause someone to be "prematurely" aged, and the same things can happen to a prolong recipient. Thus Hamish Alexander, despite being "stopped" at the equivalent of his late 30s or early 40s has steadily developed more white hair, crows feet, etc. And, I might add, that same sort of "maturing in the heat of the forge" (as it were) helps to account for the fact that Honor doesn't generate as many "Gosh! She looks like a teen-ager!" remarks as she once did. She still looks extremely young, but the strength of her will and character is a bit nearer to the skin than it used to be.