Banbury had eight balls at the final West Herts pair, but could not pull off a victory in a match reduced by 11 overs because of rain.
However, they moved out of the bottom two after Tring Park lost to High Wycombe.
Benji Hector (73) and Craig Haupt (56) laid the foundation of Banbury’s total of 231-6 in 60 overs after they had been put in.
West Herts went for the runs. But they lost wickets to the spin of Luke Ryan and Richard Kaufman and had to settle for a draw.