Package mail is considered fairly low priority, and since C-17s can only carry so much weight, mail is often bumped off in favor of cargo that is considered “mission essential.” Mail can begin piling up in Christchurch and the whole system gets backlogged meaning your package can be stuck for weeks or even months as it waits its turn in line.
The situation becomes even more dire from mid-December through late-January. As the temperatures consistently stay in the 30s or more, the runway at Phoenix, the primary airfield at McMurdo, becomes too soft to support the weight of the massive C-17s. As a result, the only flights going in and out are on the much smaller, ski-mounted LC-130s. During this “gap” in C-17 flights, all package mail deliveries halt completely.
On the other hand, sending package mail back to the real world tends to be pretty fast. I mailed some stuff back home and it got all the way to Oregon in less than a week so feel free to buy some souvenirs from the station store and send them to family and friends.
Flat mail is very reliable and fast so if you have to have anything mailed to you (like any of your medications), make sure to put it in a flat envelope of some kind. Even if it’s bulky it will still get treated as flat mail and taken down to the ice much faster.