By the 13th century, a number of things came into play that would change this traditional practice. One factor was an emphasis on seeing and adoring the Eucharist at Mass, rather than receiving it. Thus, there was more emphasis on the bread. You could see the bread, but you couldn't see the wine because it was in the chalice. The elevation of the bread after the consecration was introduced in the 13th century. (The elevation of the chalice wasn't added until the 16th century.) Receiving Communion became so rare that the Church eventually legislated the requirement of receiving Communion once a year - and "Communion" meant the consecrated bread.
By the 15th century, lay reception of the consecrated wine had all but disappeared in the Latin Church. In 1415, the Council of Constance forbid the laity to take the cup - thus making into law what for the first 12 centuries had been considered an abuse.
The rest of the Church (the Eastern Rite) continued the traditional practice of receiving both the bread and the wine.
This became an issue at the time of the Reformation - with many of the separated Churches restoring the tradition of the cup. In the latter part of the 16th Century, the Council of Trent took up the question, but made no decision.
The restoration of the cup for all the faithful in the Latin Rite would thus await the 20th century and the Second Vatican Council's Constitution on the Sacred Liturgy.
- Little White Book, Diocese of Saginaw