Thanks for all your comments. Just to make things even more complicated I put together a very simple ebook with only a few links, and my friend tells me the links work well on this ebook.
So the current plan is to make the ebook more complex in small steps until it stops working in the Kobo. Then I'll have a better idea, I hope, about what is causing the problems.
I'm afraid I can't upload the original ebook since it is a commercial ebook I designed for a small publisher in the UK. But as soon as the one I'm working on now for the MR library fails on a Kobo when it works well on the others I'll let you know and upload it for all to look at.
I understand that the Kobo uses different parts of the screen for different purposes - clicking on the centre I think brings up the menu. Is this a possible cause for the problems I'm having? The Kobo might be confused between bringing up the menu and moving to another part of the ebook.
I suppose I could put a link in the centre of the screen and see how the Kobo handles it.