The obvious thing to check is if you have FileVault enabled and attach a display simulator dongle. In the FileVault case, the machine does not restart to the OS but to a firmware / limited log in screen, but having a display connected won’t enable/disable FileVault.
You will want to have a remote KVM or someone that can log in for unexpected power failures. See this thread for a lot more options like power, display and management options for headless Macs.