The operator said it was removing some services on several parts of the North West network so that customers can have “more certainty in planning their journeys”.
About 80 out of a total of 1,500 twill not run today following similar disruption last weekend.
The areas most affected will be Liverpool, Greater Manchester and Lancashire where Arriva (Northern) said ongoing engineering projects have caused severe difficulties around the short-notice scheduling of train crews.
The biggest rail workers union has repeated calls for the operator to be stripped of its franchise.
Rail, Maritime and Transport union general secretary Mick Cash said: “Yet again today services on Arriva Rail North have been reduced to chaos as this basket case franchise lurches from crisis to crisis.
“Northern have chosen to declare war on their passengers and staff alike and they couldn’t care less about safety, access and reliability. They are a disgrace and should be kicked off the tracks.
“This nonsense about ‘staff making themselves unavailable’ is a disgrace and our members are rightly angry at the suggestion that the service chaos on successive Sundays is somehow down to them and not the company which has repeatedly shown itself as unfit to run a railway.”
Cash echoed sentiments from deputy mayor of Greater Manchester, Baroness Beverley Hughes, who has has written to managing director of Northern, David Brown.
She said: “As you are no doubt aware the Mayor has had to write to you, the Secretary of State for Transport and Transport for the North on a number of occasions over the past several months, and has also written to the Prime Minister, regarding what has been a chaotic and unacceptable situation.
“It is disappointing that once again we are having to contact you directly regarding Northern’s services failing to meet an adequate standard.”
A spokesman for Northern, said: “We are sorry that our customers continue to experience some disruption to their weekend services. We are advising anyone thinking of travelling on Sunday on these routes to plan their journey carefully.”