According to the 2001 Kansas Hall of Fame sports record book the following teams were listed for consecutive dual meet victories.

123 Kapaun years not available
*115 Emporia 1964-1978
61 Concordia 1986-1992
53 Arkansas City NA
* includes ties

This would be up to the year 2001, obviously there could be some changes. I know Beloit had 100+ wins during their heyday, but I don't believe it was enough to be #1. As to the comments of teams wrestling more duals than they used to, doesn't that apply to all records, since wrestlers get 40+ matches now as opposed to 20 in the 70's and 30 in the 80's and early 90's. Matches were very limited until we went to the 30 point system. As long as I can remember a win is a win and a loss is a loss.