After testing on my site, unfornately, i can't reproduce your problem.
Please look at my test in the following pbix.
For page1 and page2, the filter works well on different report.
For duplicated page1 and duplicated page2, I set "Sync slicer" for the slicer on the two reports, so when I make a change on the slicer of the duplicated page2, then I turn to duplicated page1, it would be affected by the slicer of the duplicated page2.
I am having this same error. I created a page with 36 visuals connected to each bookmark and 18 bookmarks total. One of them is a card with Earliest week start date in field and date in the visual level filter. I change the date filter to be relative to 1 day (leaving the today's check box unmarked) and hit apply filter. It works then when I click on a button connected to a different bookmark and click back into the previous bookmark I was on where I changed the relative date filter, the relative date filter did not save the update. I tried saving each time I made the change and still nothing.
I was also unable to make the change directly in the file on powerbi.com. Relative date filtering is working on other reports, but not on the report with all the bookmarks. I am not sure if it is a bookmark issue.