The Rapport system is you trying something different from the standard "do a series of quests for me to gain my favor" sort of reputation; however, this seems to prove more daunting the more progressed a character is in the game already. New characters are likely to complete their desires more easily than a veteran character that has already gone through most of the game. While we just started out, I think you should add a "Daily Quest" activity as something for players to fall back on as slower, but more reliable way to build up Rapport or regain back some lost ground.
I don't want to see a Blue Arrow above their head every day, add something in their dialog menu where you can ask like "Can I do you a favor?" then triggers a quest you can do once a day for each Companion, per character. Each quest you complete adds some Rapport growth to the standing with that Companion and nothing else, no gold or experience. Doing enough of these should also trigger their next Stage Quest, make it require something like a minimum of 10-15 Daily Quests to get to Stage 2, and another 20-30 Daily Quests to get to Stage 3 if you're really bad at developing Rapport the natural way.