Does Eudora require you to enter your password every time you check mail?

Try this:
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.