The only thing I can think of is what zeruyo might be referring to. Maybe, after quantizing, you have a note, followed by the same note, and perhaps the end of the first note coincides with the start of the following note, and maybe that causes Logic to sometimes play the end of the first note after the second note has started, thus cutting it off? If you have any notes like that, try trimming the length of the first one.
What I have found to work is to set the start option on the Groove Menu to Next Beat. Then have your midi notes start a 16th note in front of the bar where you wish it to start. This seems to work for me consistently. Of course, if you are starting playback in the middle of a section that already has its starting point triggered, it may not be in sync. So I tend to start playback a bar early, or even a sixteenth note early.