Windows systems that support Modern Standby can enter a low power mode while parts of the system are still active. As mentioned here or here, this can lead to a weird terminal behaviour.

As a work around PuTTY's timer could be reset just after the system wakes up from a low power mode. Display state changes can be used to trigger resetting the timer, as the display should always turn on if the user actively wakes the system.

To verify if your system supports Modern Standby, you can run the PowerShell command powercfg.exe /a and see what is listed under The following sleep states are available on this system. If you see one of these two variants your system supports Modern Standby:

• Standby (S0 Low Power Idle) Network Connected
• Standby (S0 Low Power Idle) Network Disconnected

Note that both variants can cause the weird terminal behaviour.