The most obvious thing would be to look at the Processor and Network performance tab of Windows. You may also be taxing the disk.
Probably the bigger question is, if you're really talking 30-40 stores doing this, they should be looking at a proper video distribution system and not some hobbled together Roku/DLNA/Microserver thing.
Since the performance degradation has a sharp drop at a precise number of connections (9th DLNA connection), I would explore artificial conditions, such as reaching the 10-user limit in Windows 10 Home or less.
Disk or processor performance would noticeably degrade more linearly when reaching saturation due to disk I/O or processor usage. Disk I/O would not likely cause a server connection loss.
Try logging into the server with 4-5 different user accounts, and see if the number of TVs working correctly decreases; If it does, switch to Windows Server.
Where I work, we don't rely on DLNA, rather, with a Windows PC at each sign, we can have each Sign play its own playlist, from a network share on the Win Server. Each sign can be remote controlled via DLNA, RDP, or Web client, and signs can share playlists on a common share simultaneously.
Our Company's solution includes :
(1) Win Server 2016
(1) Intel Compute Stick for each monitor
(1) Watchguard Router/Firewall
HP Aruba WAP (1 or more per location + as needed for coverage)