Ok, I contacted the support and I had a possible answer.
They suggested me to check a setting in a configuration file and possibly to change the value of that key from 0 to 1. Unfortunately, at the moment I can only do it on a couple of machines and since the problem does not always occur,it will take several days to understand if something has changed.If others have the same problem we are talking about and want to help understand if the solution is valid, we can do a much better job the more computers are involved in the verification.
To do this test, first stop the LogMeIn Hamachi service from the services screen: These are the suggested steps:
Press the Windows key and R at the same time to produce a Run box
Type in the Run box “Services.msc” and hit enter
In the Services window that appears, locate and right click on LogMeIn Hamachi Tunneling and select Stop
Then verify and eventually change the value (on my two accessible machines it was = 0), following these steps:
On your system, locate the following folder:
C:\WINDOWS\ServiceProfiles\LocalService\AppData\Local\LogMeIn Hamachi
Open the h2-engine.cfg file
Locate Core.AutoLogin and change the value to 1
Save the file
Start Hamachi again
So, if someone wants to try this possible solution, his feedback will be a great help