I doubt this is a Kali specific issue but just in case anyone else runs into it.

Host: Win8.1 x64
Guest: kali 1.06 (tried both x64 and x86)
Vbox: 4.3.6

When use "NAT Networking" network configuration in Vbox as apposed to "NAT", launching Iceweasel with the NoScript plugin enabled, will cause the network to loose connectivity to the default gateway. Connectivity will be restored in a couple of minutes.

I switched to "NAT Networking" so I could transfer files from my x64 Kali VM to my x32 Kali VM and then continued my PWK course, but my network kept dropping. I started a ping to the default gateway and noticed it dropped when Iceweasel is started. The VMs on the network could communicate to each other fine, but couldn't find the default gateway.

Starting Iceweasel in safemode - Connectivity does not drop
Starting Iceweasel with NoScript disabled - Connectivity does not drop
Starting Iceweasel without a valid nameserver entry - Connectivity does not drop
Issue does not occur when using "NAT" networking.

Wireshark shows ARP requests for the default gateway but no response until connectivity resumed. Nothing jumped out to me in the vbox log files.