I honestly do not think that this is a UI issue but it has rather evolved into a trust issue. All things considered, you clearly have a good UI because new people are actively checking their notifications.
I am not sure how long your product has been providing meaningless alerts but it was apparently long enough that people are still bitter about the experience.
My first observation is that rectifying this trust issue is going to take time so you could just wait for the user to make enough mistakes and eventually learn that the notifications are useful once more.
My second observation/suggestion is that you could implement a secondary notification which reads:
Attention, you have 1 or more campaigns which are performing poorly. Click here for details.
This could be a modal overlay or just an inline message at the top of the UI; just make it prominent and give the user a sense of "ACTION REQUIRED". Clicking on "Click here for details." should activate the notification inbox.
This secondary notification should be presented based on a combination of how important the message is and how long ago the message was generated in comparison to how long it's been since the user checked their inbox.
Important: Make sure that this notification only shows up for the absolute most critical notifications because the last thing you want is for users to immediately ignore the new notification.
I extensively use my bank's online portal which has a message center and I get about 3 messages a month and not once have I found the messages useful so now I check the messages once a year. If my bank can convince me that I am missing an important message then I will check that inbox more often.
You would think that by virtue of being a bank I would check their messages more often but, alas, here we are...