Can't get influence to work.

A Propaganda Center on the planet increases the resistance to foreign influence (never tried this myself). The Re-Education Center will prevent a planet from ever flipping, but it's a super project so they can only have one of these. Also I think that a high Loyalty racial ability (Yor 100%, Thalan 40%) helps prevent flipping.

But sometimes it just does seem forever for them to flip for none of the above reasons. With an influence ratio above 4 there's some chance of the planet flipping (except for the Re-Education Center). I don't know what the probabilities are, but it's not that unusual to have a long string of bad rolls. If you don't mind some cheese you could try saving and loading the game a few times. This does help flip planets sometimes, I think because it causes the zones of control (ZOC) to be recalculated.

Yea, they can take a while sometimes. Work a few more and you'll eventually you'll see one flip. Other than what was mentioned before, it's totally random. Sounds like you just picked 7 lucky planets.

Influence is like real farming (as opposed to farms in the game). You have to set up the right conditions and take the harvest when the fruit is ready. You set up your influence zones with starases and influence tiles on you worlds and wait to see what comes your way.
I play gigantic maps with a high influence strategy. I sometimes have as many as 30 or more enemy (and Allied ) worlds with red unhappy markers. Each time one flips, one or more other worlds become unhappy. This leads to where one or more worlds a turn flip to me (I have had as many as five at once.)
Having said that, some worlds are incredably resistant. I often end up with a small knot of 2-3 planets near the home world of each race that never flip. This does not necessarily include the homeworld itself, just the last 2-3 worlds for that race. I have never wiped out a race by influence.

David Gibb, the other guys have said it: defecting is random, and you just have to wait. I have had planets that have not flipped for game years. Other times, I have had planets flip just a few turns after getting the defect flag.

Just so you know, I have played a great many influence victory games, and often wiped out races with Influence. With that said, I did have one game where the last two races were down to 3 planets each, and they sat without flipping for so long that I decided to invade them. There do seem indicators that planets are least likely to flip when a race has precisely three left.

That is not true, I played the level right above normal, and medium map with abdunant everything, with tight clusters. I defeated 2 races out of 4 (5 total including me) and then I influenced everything else. Since it was the end of the game, all my research bases I turned then into influences and stock markets. I wiped the last 2 with influence and conquered with military (the only option that was opened.)

I agree that influence flips can take a very short time or an incredibly long time. The way I deal with influence flips is I target planets and empires that I don't want to bother warring, then go on about my current business.

For instance, maybe I'm doing pretty well but I've got a war or two eating up a good portion of my resources. There's a fairly small, non-threatening empire back away from the fighting with some good planets that I'd like. Instead of taking some military focus off the battles, I just key up a few lower class planets to build constructors. I then spend a number of turns building influence starbases near their planets until I have a fairly comfortable margin above the 4.00 mark. Once that's done I just go on with whatever else is currently happening and don't think too much about the planets I'm trying to flip.

Eventually they will flip, but they key is I'm not sitting around watching them. That gets old really fast. So unless I'm trying to play a game where I win only by influence, I just use them as a "fire and forget" type of thing. At some point they'll turn to my side while I'm busy with other stuff. It seems to work well for me and removes the tedium of wondering each turn if the planets will flip.