The notion that Christians lived under constant persecution is false. What persecutions there were tended to be local and limited. After the Neronian persecution, which lasted all of one year and affected only the Church in Rome, Christians were pretty much left alone until AD 96, when Dormitian instigated a pogrom against Jews in which a number of Christians (still identified as Jews) were caught up. Again, this persecution was limited to the city of Rome and affected very few Christians. Over the next 150 years, Christians were only persecuted as individuals, not as a movement, and then only locally, as when Pliny wrote to Trajan about what to do when Christians were denounced by their neighbors. Trajan answered that when this happens, the governor should prosecute (giving the Christians multiple opportunities to recant), but under no circumstances should the governor go looking for Christians (nor should he accept the testimony of paid informers).

The largest persecution in the period seems to have occurred ca. 175, when there was a spontaneous lynching in Lyons that wiped out much of the local leadership, resulting in Irenaeus being sent in to be the new bishop. This was not an official persecution, but a riot much like those my Jewish ancestors experienced. Like the Jews, the Christians were not hiding--which is why it was easy for the mob to kill them.

The first official persecutions took place in the reigns of Aurelius and Decius (250-255), at a time of crisis in the Empire. Wanting to enhance public solidarity, and to restore the favor of the Roman gods, these emperors required everyone to offer sacrifice both to the gods and to the imperial cult. Both persecutions seem to have been spotty and inefficient. More important, for the first time there was large scale apostasy--the Church had not been persecuted for so long that Christians, used to openly professing their faith, and not given much thought to the possibility of martyrdom, and many did indeed recant (with serious ecclesiological implications down the road).

But after 255, nothing happened for another half century, until, sensing that the Christians were becoming too large and open a movement (the church in Nicomedia was the second largest building, after Diocletian's palace) in the Empire, Diocletian imposed a second (or third, depending on how you count) official persecution.

In this case, however, he did not go after individuals but after the infrastructure and leadership of the Church. Only bishops, presbyters and deacons were arrested. A number were tortured, but only a few were executed. Mostly, church buildings were demolished, books burned, plate seized and destroyed. But the very tetrarchy that Diocletian had created to save the Empire also served to save the Christians, since not every Augustus and Caesar imposed the ban on Christians with equal zeal; in fact, in the West, Constantius I (father of Constantine) did not impose any persecution at all, and with the exception of Galerius, nobody implemented it with much enthusiasm (perhaps they realized the tipping point had been reached).

In any case, by 308 the persecution was over in most of the Empire, by 313 Constantine had legalized Christianity, and by 325 it had achieved favored status throughout the Roman world.

In short, to say that Christians only celebrated the Eucharist on Sunday because they were persecuted is not supported by the evidence.

Regarding your other arguments:

1. Breaking of the Bread is an ambiguous statement, and looking at the Greek text of Acts, one cannot say definitively that the Breaking of the Bread either occurred daily or was in fact limited solely to the Eucharist. You can't have the Apostles being good Jews one moment to justify your perspective on the Eucharist, and have them ignore universal Jewish practice the next because it does not support your perspective on the Eucharist.

2. As Taft noted, the reception of communion is not an individual but an ecclesial action, and to view daily communion in terms of your own spiritual requirements without reference to the Tradition of your own Church and the guidance of your spiritual father can have serious consequences.