Encrypted external drive usually prompts for password, despite being in keychain

Solution 1:

Two things you can try are key chain first aid and keychain reset, altough these in-house solutions hardly ever fixed anyhting for me. This is based on the fact that when some apps keep asking for passwords stored in the keychain, it's sometimes related to a corrupt keychain DB (Address Book's empty DB comes already corrupt on every new Mac - sarcasm).