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The distance will be a problem only for the size of wire you intend to run. Generally, you can run up to 100 feet for the given ampacity, but over 100 feet you would want to run one wire size larger. Any problems with a GFI would still be caused by a fault or a bleed somewhere. Personally, if it is feasable, when I install a tub, I usually run the next size larger wire anyway if the amperage of the tub is anywhere close to the ampacity of the wire. For instance 8 gauge THHN wire is good for 48 Amps, and if the tub is rated for 40 Amps, I will run 6 gauge THHN instead for 65 Amps, just to be on the "safe" side. With your length of run, nearing 100 feet, I would personally definentally run the next gauge larger than recommended. Also, don't forget that code requires a disconnect within sight of the spa, no closer than 5 feet from the closest inside edge of the tub.
(side note, THHN wire is the same as THWN, EXCEPT the voltage rating. THWN is good for 300V and THHN is good for 600V due to better insulation, which could possibly help prevent future false trips on the GFI.)
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