We can approach this question from a different angle:
Why does one make a beracha in the first place? According to the Gemara (Berachos 35a) it is סברא הוא אסור לו לאדם שיהנה מן העולם הזה בלא ברכה. This is further elaborated upon there, and it is explained that eating without a beracha is in some sense akin to stealing from God.
If this is the case, why should one ever have to make a new beracha? As soon as he made a beracha on an item one time, the item has moved from the geder of לה’ הארץ ומלואה to the geder of והארץ נתן לבני אדם!
על כרחך, a beracha acharona (as well as certain other forms of hefseik/heseich hada’as) somehow returns an item to the status of לה’ הארץ ומלואה. It is as if the beracha rishona allows you usage of the item and by making a beracha acharona you are “returning” it to God.
If that is the case, then if you made a beracha acharona (“returned” the food to God) but had in mind to continue eating rice (did not include it in the “returning”) then the rice is still “yours” – והארץ נתן לבני אדם.
There would thus be no reason to make a new beracha because the whole concept of a beracha is to appropriate something from God’s domain and make it yours, which would be completely superfluous if the thing is already yours (due to a prior beracha).