I knew I had seen a similar question recently.  It's just not here at SMA, it was in the FineScale Modeler forum:

https://cs.finescale.com/fsm/tools_techniques_and_reference_materials/f/23/t/192973.aspx

I don't know if you use the same type of marker that the poster over at FSM does, but some of the suggestions might be useful to you.  The replies all revolve around using a solvent to dissolve the ink or other medium that has dried in the tip.