I had this similar problem, but when I tried to create a sample qvw to upload for my own question I downloaded the latest version (12.10 at this time) of QlikView.
In that version I was actually NOT able to recreate the problem, so it might actually be that you are on older version that has this problem. I have definitively had it several times before att different companies, so it might actually just be a version problem.
My experience has been that the typical problem has just occured for 1-value selections (like Today() or Today()-1), while it has been the Advanced Search when the result has included more values, e.g. >=TODAY()-30.
(One workaround I have previously worked with is actually to export the faulty bookmark, modify it in Notepad and import it.)
I know this thread is dated, but I just came across this (again) and remember I solved a few years ago and I'm sure others may find it useful. Clever Niklas, for solving this by editing the XML of the bookmark directly, I thought I was the only one who did crazy stuff like that 😃
The default behavior in QlikView is that, if a search string returns one and only one value, the literal value will be stored in the bookmark as opposed to the search string. The BC_SearchOnlyOneValue Easter Egg can be used to change this behavior. This can be changed in the Settings dialog in Desktop by right-clicking the QlikView icon on the Help > About screen. Change the value to 1 to store the search string instead of the (single) calculated value.