The age of the 757 isn't the problem. There are still hundreds of these in use and they form the backbone of the US domestic network and are used extensively by other airlines such as Icelandair.
The problem is the fact these planes spend most of their time parked up and not being used. This has caused corrision issues which they've tried hard to resolve.
Maybe the RNZAF need to fly a few sectors a day for NZ or JQ when they're not being used!