I have many begonias--as well as an older one which has been around
since 2006. I keep it going by pruning and propagating.
This BIG AWB comes in for the winter. In the spring--I cut the top off of the plant and then
the stem down to near the pot to re-grow. I discard the cane-like stem. No need to keep it.
About every 3 years--I take the AWB out of the pot, root-prune it, discarding the older roots
and then re-pot it in fresh soil. It re-grows very well--and by mid-summer--I have my
huge plant back again--and, usually, it will bloom nicely as fall approaches.
I root all my Begonias cuttings in water as well. It keeps them fresher that way.
In soil--they may root--but it takes longer--and often you will lose some leaves.
Here is my OLD AW which was cut back, root-pruned and re-potted in spring.
This is taken in August--ready to pop into bloom.