Where in the change log is this explained? I had this happen Tuesday, see below:
https://forums.frontier.co.uk/showthread.php?t=158062
1.3.05 apparently eventually implemented the quite important change to reputation decay system which Sandro had announced during the 1.3 beta, but somehow got complete forgotten/omitted from the 1.3 release and the four subsequent updates. Now, as it had always been meant to ever since that announcement, reputation decay occurs for all three major factions. Since the minor faction reputation is the combined result of its individual and its major faction's reputation (only where applicably, of course; it basically considers the higher reputation of the two), and unless that minor faction is, individually, at a higher reputation than its major faction, the effective reputation goes down together with the major faction#s reputation - and up again, too, so to counteract this decay,
anything that gains your major faction rep offsets this decay entirely, for the entire major faction.
I would assume if you have a minor faction with a reputation higher than its major faction, it wouldn't show a red arrow down since the effective reputation for that minor faction doesn't change at all. It is still a bit irritating to see all these red arrows, and next to impossible for us to ever check whether the system is working properly (i.e. individual minor faction rep does not actually change) without some heavy experimenting near the reputation level boundaries, but in principle this is now in line with how reputation gains and losses have always been displayed.
P.S.: To make this clear, I still think rep decay in itself is a bad idea and should be entirely scrapped, but at least it is much less severe if happening only for the major factions, as they are much less specific in what you have to do and where, and independent factions should no longer be affected (I will test this today, and check out Shinrarta Dezhra).