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Can you please provide scripture and doctrine that explain whether our pastor can still be a pastor and church leader if he is being sued with regards to an affair he had over 10 years ago?

You are right to be concerned, because this is a very serious matter.  I see several passages relating to this situation.  In a general way, this would be a matter where church discipline would seem appropriate. 

http://www.bible.org/node/532

http://www.bible.org/node/788
http://www.bible.org/node/1545

There are texts that would appear to apply more directly to the situation you have described.  In 1 Timothy 3:1-7 we find qualifications for an elder, qualifications which would surely apply to the pastor of a church.  Among these is that he is faithful to his wife ("the husband of one wife") and that he has a good reputation among those outside the church.  More broadly, he must be someone "above reproach."  Therefore I can hardly see how this man's conduct would qualify him to remain in a position of leadership.

In addition we find Paul's further instruction in chapter 5 of 1 Timothy:
 
19 Do not accept an accusation against an elder unless it can be confirmed by two or three witnesses. 20 Those guilty of sin must be rebuked before all, as a warning to the rest. 21 Before God and Christ Jesus and the elect angels, I solemnly charge you to carry out these commands without prejudice or favoritism of any kind (1 Timothy 5:19-21, NET).

If the pastor were a man of character, he would immediately resign.  Beyond this, it would seem to me that the leadership of your church needs to act on these clear biblical instructions.  (By the way, this is not the time to let your pastor instruct you as to how you are to deal with him.)  You must be a Nathan, confronting David about his failure as a leader.  "David sinned and was forgiven," some will object, and so he was, but his sin and its consequences were very public (see 2 Samuel 11 and 12, especially 12:11-12).

In situations like this I have heard it said, "But the work God is doing here, through this man, is so important that we can't deal publicly with his sin."  Yes you can, you should; indeed, you must, if you are to obey God's Word.

You may need to seek help from your denomination (if you are in a denominational church), or from some respected Christian leader(s) outside your church.

I will pray that God will be glorified in the way your church deals with sin.

Related Topics: Church Discipline, Issues in Church Leadership/Ministry