You need to be comfortable with subdividing the beat, first into eighths and sixteenths, but as the game advances, into triplets, quintuplets, and even septuplets. Once you have mentally ingrained what those things sound like and being able to count them, then it's easier to manage when beats or sub-beats are skipped (though I don't think I've ever encountered it skipping sub-beats of quintuplets and septuplets, and I'm at level 146).

Count-singing (e.g. 1-ee-and-uh 2-ee-and-uh, etc., for subdividing into 16ths) is always a good way to reinforce that sort of thing, and that can be done whenever you are listening to music. Count-singing while listening to music with funky rhythms that syncopate on a 16th-note granularity can be particularly helpful. The game does a lot of that sort of thing.

And then when actually playing the game, I try to reinforce auditory cues with visual ones -- e.g. I focus on watching the cursor advance, reinforcing the visual feedback of it crossing beat lines with the auditory feedback of the metronome and the beat itself. Engaging multiple senses helps with retention.

May be pretty simplistic, but you have to be very aware of where the beats fall. I'm pretty intuitive about doing it, but that is one touchstone I pay attention to when the exercise is played. Good luck -- stay with it -- it get easier!