Here are three terms in 1 Corinthians 11 that I think might call this practice into question.
They should at least give us pause. First of all, nobody was ever invited to the Lord's table. The verb poieite that Paul uses here is in the imperative mood in Greek, that is, the mood of direct command. That's one reason why we call communion an "ordinance" of the church, like baptism. We are commanded to do it. In fact, NOT to partake of the supper would apparently be the violation.
Secondly, notice the word I underlined above in v. 24. This is perhaps the strongest way in Greek you can say "in remembrance of ME." We come to the table to remember, not our sins, but our Savior. Of course, if the Lord brings to your mind some sin that is in your life, the Lord's Supper is as good a time as any to repent of it and ask the Lord for forgiveness. But honestly, we believers are so permeated with sin that it is probably impossible to ever know what sin or sins remain unconfessed and unsurrendered.
This leads me to my third observation. Notice that in v. 27 Paul uses an adverb (unworthily), not an adjective (unworthy). His warning isn't about sin in general. I used to think like this when it came to the Lord's Supper: "Let's see, on Monday I was late for work for no reason. On Tuesday I skipped my morning quiet time. On Wednesday I sped on the interstate. On Thursday I spoke an unkind word to a friend. Man, this week has been a spiritual struggle. I think I'll pass on the Lord's Supper today."
No, the problem in Corinth was the congregation's failure to "discern the body" (v. 29). Paul was rebuking them because they were forgetting that every person in the room was family. There were, he says, divisions at the table. The greedy behavior of some -- they were eating their own meals and not sharing with others -- humiliated those with nothing to eat (vv. 21-23). This completely defeated the purpose of coming together as a church. "So you're hungry?" asks Paul. "Okay. Eat at home! But when you come together as a church, all should eat together. That way when you eat it will not be for judgment." In short, he is rebuking the Corinthians for their unloving, uncaring, and unworthy behavior at the meal, not because they were "unworthy."
Have you ever failed to treat your brother or sister in Christ as you ought to, as family?
A young lady was at the airport waiting for her flight when she opened a bag of cookies. After she took a cookie from the bag, a man sitting next to her did the same. This greatly irritated her. She said to herself, "How dare he?" Not wanting to create a fuss, she let it pass. But when she picked up another cookie, the man did the same. This happened time and again and she was really having to control her temper. Finally, there was only one cookie left. As she was wondering what the man would do now, he took the cookie, broke it in half, ate half of it, left the other half for her, and quietly walked off. Fuming with anger, her flight was finally called and she boarded the plane and took her seat. When she opened her carry-on to look for something to eat, she noticed that she still had her bag of cookies, untouched and unopened. Then she realized that she had been eating from the man's bag of cookies, not her own. She was ashamed of herself for faulting the man for his terrible manners. And to think that he had even shared with her his last cookie! He did not say anything but just broke the cookie in half and left.
Do you have any regrets about the way you have treated a brother or sister in Christ? Every Lord's Supper is an opportunity to choose to do better. We could probably all be a lot more loving and patient with each other. We have the opportunity every moment of every day to make a positive or negative impact on those around us. Remember: our actions reveal the kind of people we really are deep down inside.
Sproul once said, "The Lord's Supper is for Christians, not for perfect people. That we are sinners should not keep us from taking the supper." I would add: If the Lord convicts you of an uncaring spirit on your part, do not wait until the next communion service to make things right. You can do that right now, today.