Check to see what the order of the point groups are. IIRC, this can affect the way objects are displayed. Since this happens after you have shut down, I'm thinking that when you reopen, the group order resets itself and shows the points you want to hide.
In your point group, are you also including points (anything set in the include tab). What could be happening is you are including all points, and then excluding certain point numbers. This causes a conflict and excluded points will reappear.
If you want to include all points, but exclude certain point numbers, clear all settings on the include tab, and then exclude point numbers on the exclude tab.
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