Does Eudora require you to enter your password every time you check mail?
Close Eudora and open eudora.ini in Notepad. Scroll down to find the sections for your Personalities and add SavePassword=1 in each. You will be asked only one more time.
Try looking for eudora.ini in C:\Documents and Settings\Owner\Application Data\Qualcomm\Eudora if your installation is a default installation. You can also use the Windows search function to find it.