Halacha Orach Chaim 232
Someone began eating after the time he is not permitted to. Now what? The Halacha is that he may continue until close to Mincha Ketana. However, it would seem that all agree one should not do any of these activities from Mincha Ketana and on.
The Mechaber brings a solution that will allow eating after the time for Mincha has come. If the community has an appointed person that makes the rounds to remind everyone to Daven, the Chachomim would allow activities even after the time for Mincha has begun. Since we do not have this, it would seem that eating after Mincha Gedola and certainly Mincha Ketana would be forbidden. A solution brought among the Poskim is to set an alarm as a reminder, or appoint someone to remind you.
The Aruch Hashulchan tries to justify why many people are not careful with this Halacha. He writes, that most people have a set Minyan where they Daven daily. Because of this, we have less reason to be concerned with working or eating after the time one may Daven. However this reasoning is hard to understand, as we must assume there was a set time to Daven in the times of Chazal as well.

