I didn't either, but one of my (sorry) Protestant friends, the wife of a youth minister at a congregation designated "Community Church," told me that it's an issue not so much with the Real Presence, but the fact that it requires a priest to consecrate the Eucharist.
In other words, if you have the Body of Christ, you must have a priest to consecrate it. Then you need a Bishop to ordain the priest. Then you need an organization to appoint and ordain the Bishop. And before you know it, you've got a whole ecclesiastical structure (like the Catholic Church, for example :-), which some (sorry) Protestants, in the (sorry) Puritan/Congregationalist tradition, reject as "unBiblical."
As you said about some other beliefs, wagglebee, I don't agree with this position, but it makes a reasonable amount of sense, when considered with its particular historical context.
That still doesn't make sense. They had no problem saying that their ordained ministers can baptize, marry, etc. Most of them still have a form of communion. So, it seems that they still could have retained it, as Lutherans have (I won't even try to get into Lutherans' belief of Consubstantiation vs. Catholic/Orthodox Transubstantiation, because it confuses me).