Rickli, thank you for your help.
Probably, the problem was caused by the fact, that I use two CLI Accounts with the same username in nedi.conf file (but with different passwords). It looks like nedi.pl was trying to use the LAST listed pair of Username and password in the config file. After I have deleted the first listed pair of USRN&PSW and created a new pair, NEDI.PL started to use the NEW one PAIR (the last in the list)..and the one pair above stopped to be used by script.
Is that so as it should be?
Thank you, again!