A typical workflow is to select a filter, have a look at the issues, reset the filter, change the filter .....
This can be done with few clicks in current implementation.

There should be a new button "Reset Filter" if the chosen filter is preselected.

Yeah, this would be a nice solution.

I think having the drop-down list display the last selected filter would reduce the confusion in our Change Control Board ( CCB ) meetings on what we were reviewing.

The only use case for the "Use Filter" button seems to be when the "[Reset Filter]" is displayed in the list. Perhaps changed the "Use Filter" button to become the new "Reset Filter" button?

The only use case for the "Use Filter" button seems to be when the "[Reset Filter]" is displayed in the list.
This is not true. You have to push the button after selecting a filter if JavaScript is disabled.

Thank you for clarification about the "Use Filter" button.

I am trying to identify the PHP source file where code could be modified to make the list remain in last selected state. Can you provide any direction?

Can you provide any direction?
filter_api.php around line 3407 is the place where the option list of filters gets populated.
if( count( $t_stored_queries_arr ) > 0 )

I tried to fix this several years ago, the patch is in 0008069. We used that for quite some time in our local installation, but I remember that it didn't work for some filters. I cannot check, as I don't have access to that system anymore.

I updated marc's patch - https://github.com/dregad/mantisbt/tree/fix-8069

@atrol, based on marc's comment I would suggest to resolve this one as duplicate of 0008069.