Does anyone know what insufficient APC durability mean when I try to deploy my soldiers to fight zombies?

Each APC has a durability stat (like stamina). You can see it in the APC list as a number next to a green tool icon.

The max is 100. Each march you send it on costs some durability (eg 10 for a normal zombie, 20 for Wendell). If you have run it down to less than the amount you need then it will not let you do the march.

The durability will recharge over time, but its slow so you need to wait. You can do research to speed it up a little but it will still take time.