not a therory, just simple fact!
one vessel starting to kick out water of say 10+tds - norm you would just change the resin.
but with two vessels
you then plug the second one in with fresh resin.
so that fresh resin is cleaning the first vessels water from 10+ tds down to 000tds.
and as that fresh resin is only cleaning from around 10 tds it will last longer.
then
when the first vessel starts kicking out say 80 tds + then you chuck that resin.
so then the second bottle becomes the first and the orginal first bottle has fresh resin in it and becomes the second vessel .