In the Markers menu then is the option to 'Ripple Sequence Markers'.
This means if you trim or extend a clip to make a sequence longer or shorter, the markers further down the timeline will move accordingly. If you just select some clips and move them, then the markers won't move since they are sequence markers and not clip markers. This is by design, if you want a marker to be attached to the clip then you should really use a clip marker.
If you are moving clips down the sequence to create a gap for new shots, try doing a ripple trim to extend the the outgoing shot and then drag the edit point back to where it was.
There is also the option where Copy Paste includes sequence markers - you could use this but I don't think it would really help you.