edding (gloss) paint markers should ideally be stored horizontally (e.g. lying flat in a drawer) and at room temperature. This way, the ink in the filter, which is located in the marker barrel, is distributed evenly and the marker writes cleanly until empty without residues drying out in the filter.
 
Due to the open reservoir system and pump mechanism in the paint markers, ink residues can occasionally clog the nib.
This can be avoided by ensuring that after using the marker you write with the nib until it's empty and replace the cap firmly on the neck of the marker.