Welcome to the Shopify Community. Sorry to hear about the newsletters that were sent with broken links, what does your client see when they click the link? Are you able to please share a screenshot?
We did experience an issue today with some Shopify marketing emails that has now been resolved. The issue meant that some links provided in the email led to a 503 "Service Temporarily Unavailable" error. As I mentioned, the issue is now resolved, and the fix that was rolled out was retroactive, meaning any links affected will automatically have recovered and should now be working.
If this was not the issue, where is the link supposed to take the client? A screenshot of the error, as well as a screenshot of the link in the email would be helpful for troubleshooting from here. Thanks!
Hilary | Community Manager @ Shopify - Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog