I think you will have to cut off old flowers to keep the plant going. All I have seen is one strong central stem, with ever more side shoots. Can you keep doing that and have a small non-woody "shrub?"
Things I know as "perennial" have a shorter bloom period, a growing period, the tops die when frozen, then regrow from the roots. Celosia seems to behave as annual, with continuous bloom to eventual exhaustion, or a freeze. I don't imagine Celosia would be very long lasting even kept from freezing, and flowers trimmed.
Maybe this wasn't very helpful, maybe Luke can explain a little more.