Three days ago I bought a 2011 3008 HDi S-A (automatic) from an auction and was surprised to get such an immaculate low mileage car for such a good price, now I know why, on day two I experienced exactly the same problem as described at the start of this thread. I've discovered a couple of things that have helped me get round the problems but not how to fix it yet.
By taking the +ve lead off the battery for 5 minutes ( as per handbook page 190 , doors and window should be shut before disconnecting & wait at least 1 minute before starting the engine after you have reconnected) the car electronics gets rebooted, this completely cleared all the faults for a couple of days.
When the same problem came back I could only select the first three gears by using the manual gear change option (the automatic changing up through the gears didn't work at all) then I discovered, while driving around 30 mph if I select neutral then put the selector back in to position 'A' it changed up to a higher gear, I repeated this and managed to get in to top gear. Changing down through the gears doesn't seem to be affected. Although it is not a fix it has enabled me to still drive the car with all the gears.
I am keen to learn how I can fix this without blowing a tonne of cash.
Faults and Technical chat for the Peugeot 3008