What determines whether an UFO lands or gets intercepted?
While early UFOs kept triggering interceptors, I've recently had a string of UFOs simply landing despite much better satellite coverage.
Is it random whether I get to try intercepting an UFO, or do I need to improve technology (e.g. get better interceptors) so that I get a chance of shooting them down?
You get to try intercepting a UFO if you have an interceptor assigned to the continent where the UFO is spotted (this assumes at least one deployed satellite, of course, or else you wouldn't spot the UFO). To the best of my knowledge you always get a chance to intercept when these conditions are met.
Did you not have any interceptors assigned in the problem location, by chance? Or is the UFO landing before the Interceptor can catch it? If it's the latter, yes better tech can help (the Firestorm is much faster than the starting Interceptors).
As per comments on this answer some UFOs are just detected as landed (I don't recall having seen any but that doesn't mean much). If so, I'm not sure there is anything you can do if satellite coverage on the continent is already maxed. I haven't seen any detection upgrades (the Hyperwave Decoder has a completely different function in this game than in the original). So, yeah, SOL.