What all these guys said
When you start the naval progression you may have gotten progression missions relatively quickly, that is because you probably already had a lot of rep built up with a lot of minor factions, that has dried up now... and so you have to slog it out for a while. So now you need to get allied with more minor factions.
I found that once i got stuck, it took about 3-4 new minor factions to be allied with me every time I got a ranking mission.
- move from system to system
- mission for your chosen faction's minor factions until you get rep gain missions
- do a couple of rep gain missions
- get to allied with minor factions
- KEEP GOING, i nearly lost faith a couple of times, losing track of which systems had already bled dry etc.. but I got to post commander the other day
Carrying a stock of non lethal weapons and food is also a great idea as was suggested above
One last point, when you see missions for permits that you already have come up in the available but unobtainable missions section do not fret, this is a bug and it does not impact your progression at all.