Having an example plot would be helpful so that we can see what you see.
Without the picture, my best guess would be that you have enough data to enact the "Fast Marker Threshold".
From JMP Help: When the number of markers in a graph exceeds the
Fast Marker Threshold, the graph’s Marker Drawing
Mode is set to Fast. which draws dot-sized markers.
By default the Fast Marker Threshold is 50000. You can change this in the preferences (File > Preferences > Graph)
Dan Obermiller