Actually, there is no limitation or prescription given in scripture on the number of times one may partake of the bread and wine in memory of Christ. You are making an inference from the context of the first instance of this memorial at this last Passover meal. However, one may just as easily infer from scripture that the "breaking of bread" was a reference, not just to an ordinary meal but to the partaking of the bread and wine in memory of Christ.
Here are some passages I would like you to consider:
Acts 2:42 And they continued stedfastly in the apostles' doctrine and fellowship, and in breaking of bread, and in prayers.
Note that the breaking of bread is listed among the spiritual disciplines of believers.
Acts 20:7 And upon the first day of the week, when the disciples came together to break bread, Paul preached unto them, ready to depart on the morrow; and continued his speech until midnight.
The disciples came together on the first day of the week [as we discussed in an earlier question, the day of coming together is not mandated nor is it important] to break bread as a congregateion. We will see from our comments on 1Cor. 11 below that Paul tells the Corinthians that they are not to come together for an ordinary meal - i.e. if they are hungry they should eat at home.
1 Corinthians 16:1,2 Now concerning the collection for the saints, as I have given order to the churches of Galatia, even so do ye. Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come.
The first day of the week was the usual day on which the disciples came together to worship, break bread, and be exhorted from scripture.
1 Corinthians 11:20 - 34 Therefore when you come together in one place, it is not to eat the Lord's Supper. 21 For in eating, each one takes his own supper ahead of others; and one is hungry and another is drunk. 22 What! Do you not have houses to eat and drink in? Or do you despise the church of God and shame those who have nothing? What shall I say to you? Shall I praise you in this? I do not praise you. [Paul is condemning them because, although they ostensibly came to partake of the Lord's supper, their manner of doing so was completely inappropriate. He then goes on to lay out the way things should be done "decently and in order"] 23 For I received from the Lord that which I also delivered to you: that the Lord Jesus on the same night in which He was betrayed took bread; 24 and when He had given thanks, He broke it and said, "Take, eat; this is My body which is broken for you; do this in remembrance of Me." 25 In the same manner He also took the cup after supper, saying, "This cup is the new covenant in My blood. This do, as often as you drink it, in remembrance of Me." 26 For as often as you eat this bread and drink this cup, you proclaim the Lord's death till He comes. 27 Therefore whoever eats this bread or drinks this cup of the Lord in an unworthy manner will be guilty of the body and blood of the Lord. 28 But let a man examine himself, and so let him eat of the bread and drink of the cup. 29 For he who eats and drinks in an unworthy manner eats and drinks judgment to himself, not discerning the Lord's body. 30 For this reason many are weak and sick among you, and many sleep. 31 For if we would judge ourselves, we would not be judged. 32 But when we are judged, we are chastened by the Lord, that we may not be condemned with the world. 33 Therefore, my brethren, when you come together to eat, wait for one another. 34 But if anyone is hungry, let him eat at home, lest you come together for judgment. And the rest I will set in order when I come.
Note the highlighted phrase in verse 23. Paul is quoting the words of the Lord himself. The phrase "as often" indicates that the frequency of partaking of the bread and wine is flexible. Coming together as a body to do this is an important point of meditation not only on the commitment we made personally to Christ when we were baptized and also participated symbolically in the Lord's death and resurrection but that we are doing so together in fellowship with a like-minded community. We find the true meaning of the Lord's sacrifice in our willingness to serve our brothers and sisters as he did.
God bless and keep you,