I've never heard of a gin that was distilled more than once.
Multiple distillations are used for progressively selecting cuts for whiskey, Vodka, Rum, and scotch which start out as a mash.
Absinthe is not mashed. It starts out as base alcohol (which may have been multi-distilled) and has herbs added, macerated, and distilled (much like Gin).
No reason for a distillery to distill it more than once, unless they screw up and are recovering the alcohol to start over.