I tried to run the script posted above (thanks, DTLow!) and was getting "operation not permitted" errors running it against Evernote from the App Store. It looks like there's a sandboxing issue in recent macOS versions such as Mojave where Evernote can't access the files you're asking it to write. I managed to get it to work by moving creation of the file objects outside the tell block. Here's my modified script:
set pathList to {}
set fileList to {}
tell application "Evernote"
set allNotebooks to every notebook
repeat with currentNotebook in allNotebooks
set notebookName to (the name of currentNotebook)
set fileBackupenex to "/Users/oliver/Documents/Evernote/Evernote_Backup/Notebook-" & notebookName & ".enex"
set fileBackupenex to POSIX path of fileBackupenex
copy fileBackupenex to the end of pathList
end repeat
end tell
repeat with filePath in pathList
copy (POSIX file filePath) to the end of fileList
end repeat
tell application "Evernote"
repeat with i from 1 to number of items in allNotebooks
set destFile to (item i of fileList)
set currentNotebook to (item i of allNotebooks)
set theNotes to every note in notebook (the name of currentNotebook)
if theNotes is not {} then
try
with timeout of (60 * 60) seconds
export theNotes to destFile format ENEX with tags
do shell script "/usr/bin/gzip -f " & quoted form of fileBackupenex
end timeout
on error errorMessage
return errorMessage
end try
end if
end repeat
end tell