Flipping the stat around slightly, the teams we've played most in the league but never beaten are Hereford and Middlesbrough Ironopolis (both 4) and we've played Bristol Rovers away the most in the league without winning (12, 5 draws and 7 losses) but did win there in a cup game.
Hereford and Middlesbrough Ironopolis are the only teams we've played at home more than once (both twice) but never beat. There are 6 other teams we've played 1 home league game against and never beat, the only two still in existence are Cambridge and Halifax (and sort of Northwich Vics but they I believe have folded and been reborn).