I manged to get it working somehow reliably two times.
I disabled my VPN as I've read in another forum that State Saving is actually saved onto Microsoft's servers (truly horrible choice), so I figured NordVPN might be a problem.
The same post also told about the importance of choosing the same livery, as SS is tied to that also. This is not on the manual.
I noticed that sometimes the livery is pre-selected, some other times it reverts back to the default one. In the first case, I've found it's good to actually select another livery, then select the previous one manually, and some of the variables are recalled: engine health, active failures, fuel on board, windowed open, cabin thermometer. The rest is always reset (including the radios).