I recently have experienced this problem too as I am also with Bigpond. Noticed it only within the last few weeks or so. Have you tried deleting your keychain passwords? If you open keychain access and search for your bigpond passwords, delete then relaunch mail and enter your password and it may help. Seems to have worked for me (so far). I followed these instructions I found..
**Mail stores its passwords in the user's keychain, and if for some reason the keychain entry is not working properly then Mail may be sending an improper password to the server. Therefore, one approach you can take (especially if the problem happens very frequently) is to remove and reset the Mail entries. Open the Keychain Access application in your /Applications/Utilities/ folder, and then search for password entries for your e-mail account. It may be easier to isolate the password by searching for your account provider's name (such as "Gmail" or "Yahoo") and then removing the revealed password entries. Do not worry about removing the wrong ones, as your system will just replace them when you access the respective services.
After you have removed the passwords, relaunch Mail and enter your password again when prompted, making sure to click the option to save the password in your keychain.**
Hope this helps!