If customer service were telling people that the code ended on the 5th pretty sure they were wrong. As mentioned, 5th was the original end date published on most of the original official mentions of the code, but Twitter says it was extended and ended on the 7th https://twitter.com/nzpostYouShop/status/673615404409974784 .

Personally I don't really see anything wrong with the packages taking a bit longer to deliver at this time of the year. It's not like this is unique to NZ Post and as has been said, Youshop has never been sold as a super high speed service and they do tend to be cheaper than shiptoyou's USPS (depending on size and weight of the package) which has similar delivery time frames anyway. Most higher speed services are a fair amount more again depending on the exact parcel size and weight. Ship2u is cheaper, but also I don't think faster. Particularly since it sounds like they only have a shipment a week.

While paying by the 5th to try and guarantee a delivery may seem a little early, those dates tend to be earlier then they need to, to avoid complaints due to unexpected delays. Especially since they only have limited control over earlier parts of the chain (the Singapore Post run warehouse and the I presume somewhat low priority freight service they're using to fly stuff here and part of the Biosecurity & Customs checks too). And remember it's a single date, so I'm pretty sure is expected to apply to packages sent to rural delivery addresses on the West Coast (which I would guess take 2 or 3 days more) as they do to Auckland. It's also a single date for all 3 warehouses, so would be whichever is slowest. Probably China at this time of the year. From reports so far, it seems like a package paid for by the 11th or probably even later, is very likely to arrive. They simply don't want to deal with endless complaint if they don't.

My only personal complaint is 5th being the final mailing date for Christmas deliveries doesn't have to mean that the code ended then. I know last year their Black Friday code went past the final mailing date. If the problem is they found a lot of people seem to think using the code meant they should get a Christmas delivery, they could always have made a SORRYYOUMISSEDXMAS10 code to replace the LOVEFROMYOUSHOP10 code.