TLDR
VirtualBox (in my case, vagrant-managed) local-only network connections (and, e.g. NFS shares piped through them) fail when the host syspends and resumes. NetworkManager (or possibly another network managers) are interfering. If you use NetworkManager, get it out of the way by adding:
[keyfile]
unmanaged-devices=interface-name:vboxnet0
to your /etc/NetworkManager/NetworkManager.conf. (Additional interfaces can be listed after a semi-colon). If you need to read this later and get back to work NOW, try this: