Entourage keeps requesting passwords

I have been using Entourage for many years and suddenly it is requesting
passwords for all of my email accounts each time I open the program.  As
long as Entourage remains open the passwords are remembered.  When I
re-enter all of the passwords they get stored in the keychain and they are
all correct. I have run Keychain First Aid but that did not help.  It
appears that Entourage is able to write to the keychain but not read from
it.

Any ideas how to solve this problem?