I did eventually convince it by changing my password slightly on the main site, then trying again on the iPod. Was a faff, though. Then I found that it struggled with the largest of my three trees (which is still well below the 2,000-name upper limit for which Ancestry suggests the app functions best).
I'm hopeful it may get smoother as I persevere; I would love to have my tree in portable form to show to my mum when I visit her, as she doesn't have a PC.
At least it's free!
Camilla