Not sure if this is an issue or by design?
Example
Take a TDBAdvGrid, set FilterDropDownAuto and FilterDropDownCheck to True.
Run
Click the Filter Button and check 2 or more items.
Click back to the Grid.
Click the same Filter Button again, no items are checked.
Click back to the Grid, the filter remains the same.
Click the same Filter Button again, check a item and uncheck it to "clear" the filter.
I would think that the either the previously checked items should be shown as checked so you can clear them or at least if you click back to the grid it should "clear" the filter since no items were checked...
So I guess if this is by design this might be a feature request, :)
It is currently indeed not persisting these values in the dropdown checklist.
It is a good idea to have this auto persist. We'll investigate this and try to add this in a future update.