1st win7 with Remote utilities 6.5.0.8 viewer 2nd win10 with Remote utilities 6.5.0.8 host
In the power options of the 2nd computer I've chosen 30min until sleep. When the computer getting into sleep mode and reopen it, it shows the spotlight screen.
The problem is that I can't connect to the 2nd machine neither when it's in the lock screen nor when I login. I must restart the host in order to login again.
If you can't connect to the 2nd Host regardless of the sleep or login status, then the issue has nothing to do with sleep or being logged in. This looks like a general connection issue. Here are two solution guides that may help you troubleshoot the issue depending on whether it's direct or Internet-ID connection: