We had an issue where we moved into a new build and the postcode wasn't on the database. It meant we didn't receive our new V5Cs or a tax reminder.
Scary moment where we realised both cars were potentially untaxed by 2 weeks. Thank goodness we live on a private road and the ANPR van didn't come snooping around.
Anyhow we rang up the DVLA and discovered that one car was covered (luckily) because the tax was paid in monthly instalments, but no confirmation arrived by post. Meanwhile the other car wasn't covered, and and the DVLA admitted their system has an issue with not being able to generate letters to new postcodes. What I find most interesting is no other post has any trouble arriving, and Royal Mail has it on their database, so DVLA let us renew over the phone AND they looked after getting the V5Cs sent out. Oddly efficient, which was a pleasant surprise.
Best just to them up and find out what the deal is.