Mail keeps asking pop3 password even if saved

Seems to be familiar problem for most
So it seems that Mail does not recognize the fact that there is something wrong with network. It prompts the same "enter password" dialog saying that you password was rejected when there is bad network connection.
For user it seems that your password is wrong or Keychain has lost your password etc...

I changed email retrieve interval, lets see what happens.

UPDATE: so it seems that changing interval from 5 to 15 minutes did the job.