After it fails, try these in order without a hard reset: disable then re-enable Surface SMC Generic Device in Device Manager and replug; sleep and wake, then replug; full Shut down (not Restart) with cable and charger unplugged for 30 seconds; boot with the monitor already connected. Note which one, if any, restores the display.
Plug and unplug the USB-C-to-HDMI adapter 5 to 10 times. If it keeps working, the issue is the handshake with this monitor. If it also breaks, the fault is on the Surface side.
Try with the charger connected and disconnected. Try a powered USB-C hub or dock that supports DP alt mode and PD passthrough. If you have one, use an inline USB-C power meter to see whether the monitor loses power on replug.
In Device Manager, choose View > Show hidden devices and check whether a USB Billboard Device appears when the failure occurs. If it does, the monitor offered DisplayPort but the Surface didn't accept it.
Under Firmware in Device Manager, check the Surface UEFI, System Aggregator and ACPI Notify entries. Also check Windows Update > Advanced options > Optional updates, and install anything pending.
Right after a failed replug, check Event Viewer > Windows Logs > System for Kernel-PnP, USB and UCM events, plus the USB-related logs under Applications and Services Logs > Microsoft > Windows. Check Reliability Monitor too, and save screenshots of any errors.
If nothing recovers the port short of a hard reset, contact Surface support or warranty service. Give them your control tests (monitor and cables work on another laptop, HDMI adapter works on the Surface) plus the results from steps 1 to 4 and the logs.