Creating threads fails with “Resource temporarily unavailable” with 4.3 kernel

I am running a docker server on Arch Linux (kernel 4.3.3-2) with several containers. Since my last reboot, both the docker server and random programs within the containers crash with a message about not being able to create a thread, or (less often) to fork. The specific error message is different depending on the program, but most of them seem to mention the specific error Resource temporarily unavailable. See at the end of this post for some example error messages.