We had something similar - the resolution would drop to 800x600 and the screen would flash black. Do you have anything in the WIndows event logs when the issue occurs? For us, we would get dwm.exe errors and dwm.exe would terminate because the process could not allocate additional memory.  It turned out we had incorrectly configured the virtual memory settings on the parent VM.

The summary from Record the Paging File Size of a View Composer Parent Virtual Machine

            When you create a View Composer linked-clone desktop pool, you can redirect the clones' paging and temp files to a separate disk. You must configure this disk to be larger than the size of the paging file on the parent virtual machine.

Set the paging file size to a larger value than the size of the memory that is assigned to the virtual machine.

Important:

If the Maximum size (MB) setting is smaller than the virtual-machine memory size, type a larger value and save the new value.

When you configure a linked-clone pool from this parent virtual machine, configure a disposable-file disk that is larger than the paging-file size.

After setting the virtual memory to be slightly larger than the RAM and the disposable disk to be slightly larger than the virtual memory setting, the problem went away.