Fact: Many human adults have young beta cells.
When the body needs to be able to make more insulin than it is making, it will sometimes produce new beta cells. Guess what it makes the new beta cells out of?! Alpha cells, usually (alpha cells being neighbors to beta cells, and being responsible for making glucagon).
The human pancreas is generally done growing by the time it's about two years old (two years after birth, that is). Beta and alpha cells may continue to be generated anew until about age thirty, and in unusual circumstances, even later.
The beta cells do not turn into alpha cells in the event that the alpha cells are mostly destroyed source, at least not in mice.
There is currently a debate in medical/scientific/research communities about how much beta cell regeneration in type 1 diabetics matters. The question is: if we can stop the body from killing off new beta cells, can the body make enough new beta cells for it to make a significant difference for the diabetes (or perhaps ex-diabetic)? It seems to me that the answer is a pretty definite no for a lot of type 1 diabetics- the ones in which there is no real evidence of any ongoing beta cell production. It might be yes for others.