Out synched MIDI file

MIDI file looses synch when moved

I use to create MIDI tracks for each instrument I use and for each part in a song. After doing some quantizing (I prefer to do it manually) and saving the file as a specific MID file (let say Guitar1_Verse2.mid). After that I load the file and save it with another name (let say Guitar1_Verse3.mid). At this stage the notes are in the desired time synch (right on the bit). Then, I drag this piece of MIDI track to another location (which is surprisingly exactly where verse 3 begins).
When I click the ‘Piano Roll’ for editing the notes and add some variation, I always find that the notes has moved out of synch (usually in one or two grid lines and I’m working with 128 grid resolution).
What is the reason for that ? Can I do something that will enshure the correct ‘grid location’ of the notes ?

Thanks - me.