Are you sure it's OBS itself that is "going black" or is your RTSP device dropping its signal or are you experiencing network congestion? You can probably test this by having another source that is not an RTSP device somewhere on your canvas and seeing if the entire stream goes black or if it's just the source going away.
A few side notes:
- You should manually update to OBS 21.1.2. The auto-updater in 21.1.0 is broken.
- Both PCs are fairly underpowered, and it seems your straining the hardware as it is. You should probably disable the Windows 10 Game features and run as little as possible in the background,
- You'll probably want to change your RTSP device's password after this, because it's embedded in the logs as part of the source URL.