It is the 15 LY radius factor. [...]
Incidentally, this isn't the only faction where the 15 LY effect on permits is seen. I believe Peregrina also has expansions beyond the 15 LY radius, and you can't get the permit from any of those either.
Phew, so not another wrinkle in the "where do I get my permit" logic tree. Thanks.
Background: I have been trying and failing for the 4 Sextantis permit. I found two of the 4 Sextantis factions at the planetary base Akin Relay in HIP 48768 (8.72 LY away from 4 Sextantis): 4 Sextantis Inc (controlling faction) and Uniting 4 Sextantis. They are pretty much the bottom of the pile, but I managed to get them into a state where they started offering missions again by selective bounty hunting. However, even massive amounts of open/5 groups/solo mode switching did not result in a permit mission showing.
According to sysmap, the other factions in 4 Sextantis are "4 Sextantis Jet Dragons", "HIP 48165 Industries", and "Green Party of HIP 48025". The later two are around in various systems in the area, but are not offering the permit mission. I have not seen "4 Sextantis Jet Dragons" in any of the systems within 15 LY of 4 Sextantis.
So at the moment, the permit for 4 Sextantis looks to be impossible to get. I am not sure if the permit is simply not in the game, handed out by the "4 Sextantis Jet Dragons", or if this is a side effect of the currently bugged "rank" (navy promoting/engineer invite/permit) missions. I will give it another go when 2.3 goes live because this version fixes the rank missions and improves the player journal to list all factions in any system you jump into. My plan is to pull a list of all populated systems within 20 LY (normal expansion range) of 4 Sextantis, pump that through Alot's TSA, do a quick round, and see if I get more hits for the 4 Sextantis factions. If that does not work, I will re-try with 30 LY (extended expansion range).