Had same issue on my previous van, first time out from brand new had the same. It towed well and we noticed nothing until we hit the famous traffic on Bodmin. On the stop start stretch we noticed that every time we braked there would be a bump from the back. First thing I thought of was the hitch damper and did the same as the OP, tried pushing it in to see what resistance there was. In the end we got the van home without problems and checking it again on the drive, i found that although the damper seemed fine, I had a fair bit of vertical play on the drawbar. Basically, I could hold the hitch and waggle it up and down. I measured this with an engineers rule and although I cant remember the exact figure now but it was excessive (12mm seems to ring a bell). I didn't consider the unit safe to tow and thus called the dealership. Trying to explain led to a bit of an argument with the dealer, who suggested at first I was lying, then suggested I was unable to read the measure properly and it couldnt possibly record those figures. My comments to him are not fit to print here B) It was suggested on this forum that I call Al-Ko for an independent assessment, an engineer came out at the cost of £100 plus vat and instantly condemned the unit as a catastrophic failure of the drawbar. This was duly replaced under warranty.
I strongly suggest that if the OP feels the damper is fine to look for vertical play in the drawbar.