Where unity is broken by open and persistent disobedience to God's Word there is a necessity to suspend communion. "If any man obey not our word by this epistle" (2 Thessalonians 3:14). "Who concerning the truth have erred" (2 Timothy 2:18). "Having a form of godliness, but denying the power thereof from such turn away" (2 Timothy 3:5). "Now we command you, brethren, in the name of our Lord Jesus Christ, that ye withdraw yourselves from every brother that walketh disorderly, and not after the tradition which he received of us" (2 Thessalonians 3:6). Paul commands us to "withdraw from every brother that walketh disorderly." That withdrawal relates to church communion. Yet the man is a brother, a professing Christian. He is walking disorderly and breaking unity however gracious his state may be. He must be withdrawn from. "And if any man obey not our word by this epistle, note that man, and have no company with him, that he may be ashamed. Yet count him not as an enemy, but admonish him as a brother" (2 Thessalonians 3:14-15). Again he is to be treated as a brother but to publicly "note" such a man must mean church censure. "Now, I beseech you, brethren, mark them which cause divisions and offences contrary to the doctrine which ye have learned; and avoid them" (Romans 16:17)
In the context of discussing the Lord’s Supper, the apostle Paul speaks of divisions of practice and doctrine. It cannot be right that "when ye come together in the Church, I hear that division exist among you” (1 Corinthians 11:18). Yet he goes on to say in verse 19 that "there must be also factions among you, that they which are approved may be made manifest among you." There must be a distinction made between those that accord to the truth and those that do not. In other words terms of communion are necessary in order to uphold unity and order. "Only let your conversation be as it becometh the gospel of Christ, that whether I come and see you, or else be absent, I may hear of your affairs, that ye stand fast in one spirit, with one mind striving together for the faith of the gospel." (Philippians 1:27)
"Whereto we have already attained, let us walk by the same rule, let us mind the same thing" (Philippians 3:16). There is to be a unity of mind in the truth which is to be shown in Church communion. "Now I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment" (1 Corinthians 1:10)
Now the God of patience and consolation grant you to be like-minded one toward another according to Christ Jesus; that ye may with one mind and one mouth glorify God, even the Father of our Lord Jesus Christ (Romans 15:5)
Some other helpful articles may be found here and here.