Those landings are interwoven with ATC, but as ever there are exceptions to this where it just works for “reasons”.
At a towered airport the guaranteed way to get both a take off, and landing to log correctly is to first request taxi clearance by either Ground or Tower, taxi to the active, and hold short, then request takeoff clearance from Tower. You can now either fly away from the airport, and change frequency when directed, or you can request a full stop landing from where you jus took off from. Once landed, taxi off the runway, announce you are clear, and then request from Ground/Tower for taxi clearance to parking/gate. One parked at the spot you are directed to shut down the plane. You should see one takeoff, and one landing logged.
At uncontrolled fields its a bit more fiddly but still doable. You have to first announce you are taxiing on CTAF. Then hold short of the active. Slowly taxi on to the runway, then announce in which direction you are departing. Once you are in the air you can perform the reverse, announcing you are taking off. The bit that is easier here is that once you land, and taxi off the runway, you should see the ATC dialogue box instantly change to give the option to announce you are clear of the runway. Once done, you can shut the plane down straight away if you want. Again, you should see one takeoff, and one landing recorded.
Where I have seen this fail is at some un-towered airports where they probably have something funky with the way the airport was created by the AI. If you have the taxiway markers displayed, when you are announcing you are taxiing that breadcrumb trail will appear. The sim detects you are ready to enter the runway when you reach the end of that. Sometimes this part fails, and it doesn’t detect you have got to that point, so the ATC process flow never ticks over to the next step, and thus no takeoff is logged.
I wrote a post some time back where I logged as many of these stages as possible, and the responses you should expect to see in the ATC dialogue.
To cut a long story short, if you don’t jump through the appropriate hoops, takeoffs and landings “may” not be recorded. Having said all that, I have been messing around in Idaho in a tail dragger, doing landings on steep slopes on any patch of land that doesn’t have trees, and had a lot of those landings count, and I never went near ATC! I think at airports it works a little differently, but the above should assist you.