Unfortunately, no mine don't all disappear.
I did notice that if I still have new flags that they will disappear if I log out then login again, very odd.
If I read one post then use the BACK button that message flag will change but when I read every subsequent message using this technique the flags stay new.
Unless of course I use the "link" back to the forum I am reading then all read strings become read and If I still have any new ones they remain marked as new.
I did fiddle with my cookie settings last night and this morning had to log in and every time I read new messages the flags would stay there.
Finally I corrected my cookie settings and all was well again.
Fern! Have you considered creating a new user profile and seeing if the same problem persist's with the new profile? If it does then it could be a problem with your computer settings?