Greetings....When I create a Hyper-V host, I generally partition the disk space into 2 (C & D). Usually, creating the C drive for the OS only and the D drive for the VM's and VHD's. When sizing, I have been allocating 65GB to the C drive, which normally is enough.
It seems as though the C drive is getting down to 3GB after some time, and I am not sure what files / data is being written to it. I am 100% sure that the VM config and the VHDs are on the D partition, and not on the C.
There are probably other things on the C: drive such as your page file. You can move the page file to a volume with more space and gain some back on C. Also, if you're using DPM for system state backups, you might be eating a lot of space for those files. Finally, depending on what you have installed - such as IIS - you might have log files being written to C: as well, but those, too, can be moved.