I think this is fixed in 2.39.7. It only occurs in certain situations (see below).
You’ll need to check the setting ‘load maps last’ in the MapPress settings in the new version.
Please let me know if it works for you.
The problem seems to occur only with Firefox, and only when a map has satellite imagery.
In this case it seems that Firefox needs to have the maps loaded later than the other browsers.
Google recommends the body ‘onload’ event but MapPress displays maps immediately (so they won’t be delayed or blocked by other scripts or iframes on the page). The new setting loads the maps using the jQuery(window).load event, which should be roughly equivalent to ‘onload’.