Comment by TuringTest

Yes, I allowed background running in the power saving settings - this helps in the short term.

But the problem seems to be in the server; after restarting the computer or the phone, the connection between folders seems to be lost - it doesn't "see" the remote folder anymore, even if its ID has not changed.

To be fair, this doesn't happen with Syncthing only. Other tools like Nitroshare or Dukto are also hit or miss when trying to connect from the phone.