Just wondering if there is a way of stopping this every-time P3D runs?
Your subject refers to the "Indexing Airports", which seems to be the kind of wording used by the SIM ITSELF to recreate the cache. Of course, if the sim itself has recreated the cache, it means something has changed in the Scenery Library, otherwise the sim wouldn't do that. And if the sim has reindexed the airports, it's to be expected that GSX will do the same, and it would be wrong if it didn't.
If, instead, you used the "Indexing Airports" term liberally, so the SIM wasn't really indexing its cache, and you are ONLY seeing the message from GSX (the RED text on the top), which says to wait while the airport cache is being rebuilt, than it's another issue entirely, and it might caused by a problem such a corrupted scenery file, that you might be able to spot if you enable logging in the Troubleshooting section of the GSX Settings menu, and check the Couatl.LOG file for any messages that might indicate a problem while recreating the cache.