You can restart at page, spread or section level. Did you check if there starts a new section?
Thank you for your reply.
Where do I control this restarting? And what does the hidden sign look like that indicates such a re-start?
In the page panel a new section is indicated by a small triangle upon the page symbol where the section starts. Either click twice there or in in the panel menu.
Footnote options are found in the Type menu > Footnote Options…
Yep, I got it now. I went to the Manual (as a last resort :-) and found a description of how to remove all sections and then started over from scratch, inserting new sections and told InDesign to start new Footnote Numbering at every section start. Works like a charm!
The problem was that InDesign created a lot of random sections from my imported Word document (.doc) – sections that wasn't present in the original Word document. Anyway, it's sorted now, and I'm grateful that you pointed me in the right direction. Thanks!