Comfortable Working of Selection Tool After changing the hotkey "Selection" tool began to work by clicking the Left Mouse Button+Ctrl/Alt (Select/deselect). I'm just fine with that, but there is one catch:

If use the Border Selection outside the object (LMB+Ctrl or Alt) this tool is working correctly, but if using it  within a object, before created selection is cleared.

For example:
If I need to add additional polygons to the current selection

1)


2)


What I need to change or add to this tool works correctly within the current object and  active selection is not reset?

Current HotKey:
There is probably nothing wrong with your Border Select key definitions, its probably the Select/Activate operator that is resetting your selection.

Try change it to either to a Mouse Release event or to Extend Selection by default, so there's no conflict and starting a border select won't unintentionally trigger the colliding operator.