virtualbox.org

I have created a Linux Debian 8 VM to run Docker containers, using Vagrant and VirtualBox as provisioner.
It is running fine on linux hosts, windows 8 hosts, and a couple of macs we have, but it consistently crashes on two other macs which one of our partners uses.

The symptoms are: the VM halts as soon as we run some specific commands, most notably 'apt-get update'.
It also used to hang when running 'docker pull'.
Then we upgraded the base image from Debian 8.0 to 8.0.3, and it got a bit more stable: now we can get 'docker pull' to finish, but 'docker run' crashes it.
Downloading random stuff from the internet works, as well as running 'apt-get upgrade' or 'apt-get install'.

I have checked the logs inside the VM and found no trace of specific errors.
I have tried running the VM without the vbox drivers installed, and also with a newer version of the vbox drivers (4.3.12 -> 4.3.26).
I reduced the number of virtual processors from 2 to 1, and set memory to 1GB.
But the vm keeps crashing.

Does anyone have an idea of what could be the cause of the problem?

The mac which I tested yesterday, and had problems, had vbox 4.3.26, and macosx lion.
The two macs which had no problems had different versions of macos and of vbox.

Before going further, please reproduce the issue only using VirtualBox in a VM you created yourself, not using Vagrant or Docker.
If you manage to reproduce the problem, then provide the VM log files and the guest settings as described here.