Dorico itself doesn’t perform any license checks after it first starts up, but the audio engine, which is a separate process and which runs alongside and in partnership with Dorico, does check its license more often, including while the application is running, and if the license check fails because the eLicenser is unreliable on your system, then Dorico is liable to hang and possibly eventually to crash because its expected communications with the audio engine will fail when the audio engine itself fails its licensing check.
This is obviously an unacceptable state of affairs and is one of the many reason why we are retiring the eLicenser system at the first opportunity, which will be early next year with the release of Dorico 4. I can only apologise for the poor experience you are having in the meantime.
Do you have a USB-eLicenser to hand? If so, I could try sending you a time-limited activation code that you could install on the USB-eLicenser to see if that makes the licensing behave more stably on your computer.