What does it mean when iMessage suddenly stops saying "Delivered"?
iMessage will not return a "delivered" message if the message was not delivered to the user.

Here are some situations of iMessage returning different statuses:

Not delivered (usually accompanied with a red exclamation): the message could not be sent from your phone due to your network connection

(no message): the message was successfully sent from your phone, but not delivered to the recipient due to the recipient's network connection 

delivered: the message was successfully sent from your phone and delivered to the recipient.