I've read this before and it confuses the hell out of me in the case of single batteries, as there was mention of similar effects as twin batteries but the front 1 failing, if the single battery couldn't cope with unlocking the van i really wouldn't expect it to start the van which takes considerably more power
But i personally would go with checking your key fob, it is rechargeable but may not be holding, that said tho I'm going on the idea that you can get enough power from it to single unlock the front doors but then it goes flat on second press.
If that isn't the case then it must be ghosts
Have you got a spare?
Also the battery should be replaced anyway i think, the radio turning off quickly it's a good sign that the battery isn't good, you can get it drop tested at most decent garages.
56 350 2.2 130ps mk7 with 2 side doors
65 290 2.2 125ps custom with 2 side doors
07 350 170ps
Ids v86 licence + v86.04 update + xprog
hereIds map
here