The side probably had its best chance to get a win when they took on fellow strugglers Buller-West Coast, in a one-day game at Aorangi Park yesterday.
On a batsmen-friendly pitch, the South Canterbury bowlers struggled to keep the pressure on the visitors, who managed 250 from their innings.
Having been rolled for just 65 in their last match, the target seemed a tough one, but South Canterbury started positively, being 60 for one early on.
But when top-scorer Jack Harper was trapped leg before wicket for 42, South Canterbury were left wondering what might have been. They fell 30 runs short.
The zone tournament also involves teams from Canterbury Country, Mid-Canterbury and two metro club teams from Christchurch.
Games will continue today around South Canterbury.
The tournament will be completed tomorrow.