When I try to add an email address (by clicking on the address and slecting the 'Add to Address book' option the email addrss does not stay in my address book
When adding an email address to my address book often it will stay in the address book until I close Thunderbird then it disappears and it won't pop up as a valid address when I am composing a note.
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This usually means that the address book data file is corrupt.
I'd suggest you export your misbehaving address book to an LDIF file, delete the original address book then re-import its data from the LDIF file.
Note that you won't be allowed to delete either Personal Address Book (PAB) nor Collected Addresses (CA) within Thunderbird. You'll have to close Thunderbird, open its profile and delete:
abook.mab for PAB, or history.mab for CA.
When you next run Thunderbird, it'll create a new empty address book to replace the one you deleted. Import your address to a new temporary address book, then move the Contacts (drag-and-drop) into the preferred address book.