You could try to create a new email account, then in the message template that is not working, change the email account to this new one.
Save the template, then go back and edit it to put back your main email account, then save again.
I've also fixed problems by looking at the table directly in SQL, by listing a known good record with the one not working and comparing the values of all the fields in the record...
If you are familiar with SSMS, you can run this query on your database, this won't change anything, but you can see if the values look different and report back here.
use [enter DBname here]
SELECT *
FROM [MessageTemplate]
where Name in ('OrderPlaced.CustomerNotification', 'OrderPlaced.StoreOwnerNotification')