Using default flightplan interface, I flight a leg from LIMC to ENGM and at landing the Logbook updated correctly. After Logbook updated I continued the flight at gate. After an hour I planned a second leg directly into FMCG from ENGM to LIMC.
After takeoff my flight was as espected and the aircraft landed at LIMC.
At gate I set cold & dark and the map of Logbook poppedUp but with fields Takeoffs & Landings set to “0”. (FS 2020 version 1.11.6.0)
I think this is what happens when you press “continue”, whether by design or due to a bug. To be sure of logging a flight, you need to exit back to the main menu, then start a new flight.
If it is a bug, I doubt if it’s very high on their list of priorities so won’t get fixed soon (if ever).