Thornton went down by six runs to Mytholmroyd. Mark Higgins took four for 33 as the home side reached 227 for nine in their 45 overs.
Thornton's reply got off to a good start with Andy Hutchinson (49) but a middle order collapse stalled the chase and despite a late flurry from skipper Greg Soames (30) they fell just short on 221 for nine.
The second team brought their losing run to an end with a ten-wicket win at Southowram.
In the following day's Keighley Cup quarter-final at Crossflatts, skipper Soames (84) set up a thrilling finale but with 11 needed to win off the last over, Thornton could only score nine.
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