I want to know is there a such thing as a gas that can be reburned multiple times?
In short: There are no compounds that can go through complete combustion more than once.
Incomplete combustion products, like carbon monoxide, can be burned to give the complete combustion product $CO_2$. This would however then not be the same gas as was (incompletely) burned to give the carbon monoxide.
As bon mentioned in his comment: a compound can never be burned twice, since if the product of the reaction would be the starting material and energy were to be expected to be released, as with a fuel, then energy would come from nothing, since no chemical change would have occurred.