Question: My large application user base means we're constantly having a steady stream of users with hard and soft bounce issues as we send them broadcast emails.

We're building some internal tools to make it easy for staff to follow up the hard bounces via alternative channels, however maximising self-service is preferred.

What's the best way to tell a (non-technical) user via an application interface 'hey, we noticed your email address hasn't been working since $date because it's been throwing the error $error' in a useful enough way that won't cause the user to freak out and take meaningful action?

Often ESPs will be provide transient false hard-bounces also, causing our system to back off and internally black list the email service for say 7 days. Is it worth providing a UI to the user for them to remove their address from the internal blacklist and resume email sending? Or am I looking at this wrong?

Yours, a humble web sysadmin and email guy.

[edit] - perhaps I should force the user to re-validate their email address in order to get themselves off our block list early?

Answer: 
**You're on the right track.** Let the user know that emails from the system have gone undelivered and provide a link to the account page where they can check the address on record. Use your standard in-app notification mechanism so it's familiar. Simple, actionable messaging is always welcome.
I see this as a great opportunity for your sales team (assuming this is a paid app). 

Sure, you could add an alert. Some people will update their info. Most won't. Or, you could call them. Yep, use a phone.

Simply call and say, "Hi, this is XXX from YYYY. We noticed that your email address we have on file might be wrong and we can't send you emails. Would you mind giving me your email address?" Now, you have another chance to upsell, ask for feedback, get referrals, testimonials etc...

Of course, this assumes you have their phone number.

Another option would be asking them to update their email address on their next login. Simply add a secondary step to the login process. If the email address is invalid, route them to the "update" page and ask them to update it. Hold their hand and walk them to the exact form field they need to update.