I've been growing cayenne peppers on a bedroom windowsill for years now, usually keeping the same plants for 3-4 years before starting again, and they flower and produce all year round, albeit not as quickly in winter (they must be one of the easiest and long-suffering chilli peppers there is.)
I don't re-pot mine at all in between re-sowings, although they do get a tomato feed from time to time to keep them happy.
Re-potting yours might make them temporarily forget about flowering and start producing only leaves again.
Other opinions are no doubt available!
