Here's one theory. One of the known side effects of paxil is somnolence, excessive sleepiness. Any sleep-inducing preparation can cause gout in an indirect way by exacerbating sleep apnea, the condition where muscles in the pharynx relax so much during sleep that they allow the airway to close up repeatedly for prolonged periods. Sleep apnea causes gout by two effects resulting from the lack of oxygen. First, the oxygen-starved cells in the body begin a process of disintegration (catabolism) which culminates irreversibly in their generation of excess uric acid fed into the blood. Second, the percentage of carbon dioxide in the blood is increased, which makes the blood more acidic and hence less able to hold uric acid in solution. As a result, uric acid precipitates from the blood in the form of monosodium urate crystals. When these crystals lodge in a joint, they cause a gout attack.
I had a similar experience when I started using melatonin before bed every night. It took me a while to realize that it was exacerbating my sleep apnea, resulting in renewed attacks of my gout. When I cut out the melatonin, my gout attacks ceased, along with my wife's complaints about my excessive snoring.