Solved! In Mac's Keychain I had to change manually all access privileges for the mail accounts and to give it free to "any programs" - which is not the safest way, but no more annoying by the obvious PowerMail 6.1.1 bug.
>Oh my gosh! >Since this update to 6.1.1 PowerMail asks me _every_ time if I will >allow the program to have access to the confidential information on my >Mac key ring! Allways and before connecting to the mail servers. >And of course I've given the permission several times "for ever". But >PowerMail disregard it. >What can I do to stop this annoying questions once for ever? > >

