I hope I understand that correct, you start a process and then stop it. Then you start it again. This means the process group instance has to be the same on the Dynatrace side. It just shows a short period of unmonitored state within its availability chart,
We simply can't say if the process group instance is terminated forever, as we don't know in advance if the user starts the process again.
What you can do it to check its 'lastSeen' timestamp in order to find out when Dynatrace did last time receive any monitoring information from that process.