The Huntington Road club are looking to bounce back into division one at the first attempt, but they went down 92-62 to Doncaster, losing all four rinks.
At home, Barry Johnson’s side were 15-11 behind with three to play but lost by only one shot, 16-15.
Bill Waldie’s side were made to pay for a poor second half, which saw them go from 10-10 to a 25-11 defeat.
Away, Ralph Tiplady’s team were also left frustrated. They trailed 20-17 at one stage and were edged out 22-21.
Bob Edwards’ team were left playing catch-up at 14-7 down after five ends and they lost 29-19.
New Earswick’s disappointment was eased as their Hebden Trophy team continued with their impressive start to the season.
They made it three wins out of three to inflict York’s third defeat in four games.
Their 81-78 victory saw them pick up 12 points.
At home, Geoff Walker’s team led 3-0 after two ends. However, Bob Howland’s men hit back in style to take 14 successive ends and a 21-3 lead.
That proved enough as, despite a late rally by Walker’s team, they took the points from a 23-11 success.
Graham Jones’ side also had a good winning run, losing only one end to Eric Hodgson’s team between the tenth and 19th ends as they moved from 7-6 ahead to lead 21-8 en route to a 23-12 victory.
At Thanet Road, it was the home sides who enjoyed more success with Tony Bryan’s rink leading 9-1 after five ends against Brian Birch’s side.
They finished with a four then a three to win 30-15.
Jim Robertson’s team also got off to a good start, leading 13-1 after six ends.
Although Graham Storey’s side came back well to 22-17 with two ends to play, swapped threes gave the home side a 25-20 win.