Gas has been detected in a number of debris disks. It is likely secondary, i.e., produced by colliding solids. Here, we report ALMA Band 8 observations of neutral carbon in the CO-rich debris disk around the 15-30 Myr old A-type star HD 32297. We find that C-0 is located in a ring at similar to 110 au with an FWHM of similar to 80 au and has a mass of (3.5 0.2) x 10(-3) M-circle plus. Naively, such a surprisingly small mass can be accumulated from CO photodissociation in a time as short as similar to 10(4) yr. We develop a simple model for gas production and destruction in this system, properly accounting for CO self-shielding and shielding by neutral carbon, and introducing a removal mechanism for carbon gas. We find that the most likely scenario to explain both C-0 and CO observations is one where the carbon gas is rapidly removed on a timescale of order a thousand years and the system maintains a very high CO production rate of similar to 15 M-circle plus Myr(-1), much higher than the rate of dust grind-down. We propose a possible scenario to meet these peculiar conditions: the capture of carbon onto dust grains, followed by rapid CO re-formation and rerelease. In steady state, CO would continuously be recycled, producing a CO-rich gas ring that shows no appreciable spreading over time. This picture might be extended to explain other gas-rich debris disks.