Why do I have to reenter my password to send or reply to a message when I just entered my password to get new messages???

Connecting to server to download mail uses either Pop or Imap protocols, but sending is done via SMTP server - not the same.

Do you have Thunderbird set up to remember your Password for the account ? When you enter password at the prompt - did you also select the checkbox telling Thunderbird to remember the password? Have you checked your Settings > Privacy & Security > Saved Passwords to see if you need to update/edit any old saved passwords ?