A "problem" I have had, has been that after selling my exploration data I ended up being Allied with the Empire and all the minor factions affiliated with it. This can have the curious effect of preventing you from getting more ascension mission. Many others have commented on that situation, as far as I can tell its a bug, and I am hoping it will be fixed in 1.3.
You can still earn rep with the minor factions.
I found that when I became "Friendly" with the Empire, all the minor factions moved up one step so the Neutral ones became friendly and the friendly ones became allied.
Same thing happened for the Allied level.
So it seems you rep with the major faction plus minor faction.
However the rep with the minor faction is recorded separately and moves up down separately we just cannot see what it is unless it is drastically different.
I haven't tried it but I assume if you were allied to a minor faction and became unfriendly with its major faction you would drop to Friendly.
If so what we need is a way to see our unmodified local rep, so we know we can work on improving it regardless of our over faction rep.
I think this is one of the reason why people think their promotion progress is stalled, they get allied with the Major faction, become "allied" everywhere and done realize they still can improve their Local faction reputation and earn progress towards getting offered the next promotion mission,
However if you are no longer getting
any missions, that will be a bug