Why must the Lord’s Supper be taken every week?

Answer:

"For though you might have ten thousand instructors in Christ, yet you do not have many fathers; for in Christ Jesus I have begotten you through the gospel. Therefore I urge you, imitate me. For this reason I have sent Timothy to you, who is my beloved and faithful son in the Lord, who will remind you of my ways in Christ, as I teach everywhere in every church" (I Corinthians 4:15-17). Paul also commanded, "Imitate me, just as I also imitate Christ" (I Corinthians 11:1). And, "The things which you learned and received and heard and saw in me, these do, and the God of peace will be with you" (Philippians 4:9).

Thus we learn that the examples recorded in our Bibles are not just illustrations or suggestions. We are expected to follow the approved examples ("as I imitate Christ"). Obviously, there are examples in the Bible of people violating God's law. These examples are not binding, in that we are expected not to follow these examples, but learn to avoid making the same mistakes (I Corinthians 10:6). "Beloved, do not imitate what is evil, but what is good. He who does good is of God, but he who does evil has not seen God" (III John 11).

There are three types of good examples found in the Bible:

1. Something is commanded but we find a variety of examples of how that command is carried out. An example would be Christ's command to go into all the world (Matthew 28:19). As we read we find the disciples: Running (Acts 8:30),  Riding in a chariot ( Acts 8:28-29, 31), Sailing on a boat ( Acts 13:4), Walking ( Acts 20:13), etc. Thus we conclude that no specific way of going is required, but we are required to go.
2. Something is commanded and we find specific examples of how that command is carried out. An example would be the command to give cheerfully (II Corinthians 9:7). We find that they gave liberally and willingly (II Corinthians 8:1-5), they held nothing back (Acts 2:44-45), and they did not count their possessions as their own (Acts 4:32-35). Each example shows the command being carried out with the same attitude. The lack of variance indicates there is no other way to carry out the command.
3. Something is not specifically commanded, but specific examples exist. Here is what you asked about.

"Now on the first day of the week, when the disciples came together to break bread, Paul, ready to depart the next day, spoke to them and continued his message until midnight" (Acts 20:7).

When Jesus instituted the Lord's Supper, he only mentioned that it was to be done, but he didn't mention the frequency. We have one example that does mention the frequency, and that is in Acts 20:7. When examining an example it is important to ask whether the stated fact is incidental or important to the subject at hand. In this case, we are told that the Lord's Supper was taken on the first day of the week. The phrase is qualified so that we as the readers know that the first day of the week was when the disciples came together to break bread (that is, partake of the Lord's Supper). The word is such that we cannot conclude that the partaking of the Lord's Supper was on the first day of the week by coincidence. This is the day when the disciples took the Lord's Supper. Thus it cannot be ignored. Nor are there any commands or examples in the New Testament which tells us that any other day was used besides the first day of the week. Thus, we conclude that this approved example binds us to only partake of the Lord's Supper on the first day of the week.

But your actual question is: Which first day of the week? Again, the wording is clear, though some would like to make it obscure. If I hired a man and said: "Friday is the day we hand out paychecks." Would the man conclude that he gets paid once a year, once a month, or once a week? Obviously, he concludes once a week. Why? Because every week has a Friday. Now the disciples gathered on the first day of the week to partake of the Lord's Supper. Should we conclude that they did it once a year, once a month, or once a week? The answer is the same. Every week has a first day, thus the wording means they gathered each first day of the week to remember the Lord's death. To get any other frequency would require adding something to this passage that is not there.