It would be very valuable to maintain historical relationship data. For example, Bill chaired our membership committee two years ago and Sally chaired it three years ago and as such might have ideas and experience to share with Pat (this year's chair).
Another example: Tom used to work for Target and now works for Disney. When we search for people to contact Target for donations, it might be nice to show not just current employees, but former employees as well.
Final example: Lucy was Director of Engineering at Lincoln Labs. Gary, the new CEO at FooBar, Inc, used to work at Lincoln Labs (mentioned in his bio). When approaching him about sponsoring our registration drive, it would be good to see if Lucy (his former boss) has any insight on him.
This has a companion requirement of being able to easily purge relationships older than a certain date.