Your Hyper-V virtual machines may be happily running along, when suddenly they go into a "Virtual machine state : Paused-Critical" condition. If you resume them, they run for a few seconds and then pause again.
This happens when the volume hosting your dynamically expanding VHDs runs low on disk space.
Either free up space on the host volume, move one or more VHDs to another volume with sufficient space, or free space in the child partition and compact the VHD.
To compact a Hyper-V VHD, shutdown the virtual machine and open its Settings. Select the VHD and click the Edit button. Select Compact > Next > Finish.
Ben Armstrong also has an excellent article explaining how to compact a VHD file using PowerShell or VBScript.