Here are two states you don't want to find your Hyper-V virtual machine in and what to do about it if you do.
When a Hyper-V virtual machine is in the state 'Paused-Critical' it commonly means that a host volume where a differencing or dynamic disk is located is running out of space or may already be full. To avoid crashing the the virtual machine it will automatically put it in a paused state called Paused-Critical.
To resolve this free space on the drive and attempt to resume/start the virtual machine.
'Saved-Critical' generally occurs when the virtual machine configuration files can not be found. They likely are deleted, moved or corrupt.
To resolve this issue find/fix the configuration file. If it can not be found or fixed create a new virtual machine using the new virtual machine wizard and attach the existing VHD's. Note that recreating the virtual machine will not bring back your snapshots or saved state information if you happened to be using them on the virtual machine which lost its configuration files.