Can Southern Baptists take communion at home alone? There is an old man in our neighborhood who is a member of a Southern Baptist congregation, though for various reasons he does not attend the local church. 

He asked me what I thought about the question, "Might a person read the Scriptures, remembering Jesus and the Cross, and take communion (the wine and the flat bread) alone at home, by one's self?" He reminded me that various wealthy people throughout history had their own chapels, priests and attendants that served the communion supper, "at home alone." 

Do the Southern Baptists have a position on private home-communion?
While I am unable to find any evidence that the Southern Baptist Convention definitely supports the practice, there doesn't seem to be any reason for them to do so.  For one thing they/we believe in the "priest-hood" of all believers, so there's no requirement that communion be administered or overseen by an ordained minister.  In their "Basic Beliefs" web page, they state: "The Lord's Supper is a symbolic act of obedience whereby members … memorialize the death of the Redeemer and anticipate His second coming." Here's a link to that page: http://www.sbc.net/aboutus/basicbeliefs.asp

Each congregation decides how often they will observe communion as a congregation, and while there is never an implied injunction against extra communion services by "sub-groups," the expectation would be that all who partake are verified members of the church by baptism.
On an anecdotal note, my SB minister of many years would often observe a communion for himself alone before he began bible study.