Captain Fee 2248-2379 131 years
Captain Thompson 2380-2520 140 years
Captain Brace 2521-2645 125 years
Captain O'Brien 2646-2774 128 years
Captain B. McCrea 2775-
The events of WALL-E occur 700 years after the Axiom leaves Earth in 2105. The captains are very long lived, perhaps due to the microgravity, which appears to have offset any decrease in longevity due to obesity.
If these are the beginning and ending dates of the reigns as captain, as the non-overlapping dates imply, then the captains live very long indeed. Captain McCrea has been captain 30 years by the time of the events depicted.
UPDATE: though I copied this from the film that we have been watching over and over again with Linus, it turns out there is a FAQ with this information.)