No idea of how to diagnose your problem but we had pretty much the same kind of thing happen just after we moved to our new house, it had a new Vailant combi fitted but still had the old timer which was quite old but was showing signs of working intermittently, we had out the British gas service guy and he said 'it could' be the timer switch that's not playing ball with the combi but couldn't be 100% sure so we changed the timer to a 'HIVE' unit... absolutely brilliant bit of kit.
Not helping you at all really I know but it's an option if you can't sort your timer out.
I thoroughly recommend the HIVE gizmo, we have it linked to our mobiles, lights, ALEXA, ( and I'm a proper technophobe). which is a bit surprising... given my 'user name'
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