Same problem, the reprogramming worked, here is a walkthrough
I found this thread in July 2013 when I found two lowly Dodges had the same problem with a Genie rolling code opener. Be sure to read your owner manual for vehicle-specific clearing/training for the Homelinks. I'll cite two examples, #1 a 1998 Durango and #2 a 2009 Challenger.
This should work:
1. Hold down the learn button on the door opener until the red LED flashes rapidly. It will seem like a long time, probably around 20-30 seconds. This clears the opener's memory.
2. I used two handheld remotes to program, one for each vehicle. You must use one of these to train your Homelink. I'm not sure if you can use the same one, so I used two remotes. I may have this out of order, you may be able to train the Homelinks before you cycle the doors, but what I wrote here worked for me.
3. For remote #1, press the opener learn button on the opener, then the button on the remote you want to use for that door. Press the remote button again (if you can watch the opener LED, you should see it go from flashing to solid). A third press will turn off the opener LED. A 4th press should work the opener.
4. I then used remote #1 to program vehicle #1. I held down the outside two Homelink buttons to clear all codes. On vehicle #1 there was an LED that flashed faster once cleared, vehicle #2 had a dash message in the vehicle info center.
5. To train the Homelink button for vehicle #1, at the same time I pressed and held both the programmed button on remote #1 AND the Homelink button I wanted to work this door. The door cycled while doing this since this remote was trained. On vehicle #1 I got a LED training confirmation by rapid flashes, on vehicle #2 a "trained" message on the info center.
6. I then activated the learn button on the opener again, and pressed the Homelink button I had trained a total of 4 times and the door cycled.
7. Repeat steps 4~6 using remote #2 for vehicle #2.
Your mileage may vary, but this should do the trick. Hope it helps another frustrated Homelink user in the future!