debian 8 VM keeps crashing

[gggeek]

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I have tried running the VM without the vbox drivers installed, and also with a newer version of the vbox drivers (4.3.12 -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.

[noteirak]

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.