Reconcilling a Broken Christian Marriage

I was thinking about Christian marriage and remarriage a little tonight and this verse popped to mind as I was considering two people who are divorced and yet both attend my church.
23 So if you are offering your gift at the altar and there remember that your brother has something against you, 24 leave your gift there before the altar and go. First be reconciled to your brother, and then come and offer your gift. - Matthew 5:23-24
I believe that a professing Christian husband and professing Christian wife are to remain together, despite their problems, as long as it is physically and emotionally safe to do so. Because we live in a broken world there are times when even Christian people need to split up, temporarily or permanently. The permanent option, however, is a drastic step that should only be taken after much prayer, counsel and thought. I would go on to argue that in occasions where a marriage must end, at least one of the two partners are not even truly Christians.

So, what about the couple at my church? They are friendly and kind around one another at church. They both attend regularly and even serve in some capacities around the church. But their marriage is unreconciled and it doesn't appear that either party is moving to rectify things.

So, should they take communion? Should they be allowed to serve in the church? What would you do if you were an elder at my church?