No prompt for password even though Logon security set to none

[Anne]

We have users who have access to several mailboxes;
therefore they change profiles several times a day. All
profiles are set up so that a password is required.
However after logging into one and then the other a
password prompt does not come up - the mailbox opens
automatically.

A reboot will solve the problem, almost like a service is
finally stopped. Does anyone know how this can be
resolved? Thank you!