Currently, when Dreamhost notifies customers about potential ICANN verification, it does so through the Dashboard/Panel and e-mails sent when a customer registers a new domain, or changes the domain's registration info.
Verification e-mails for ICANN are sent to the registrant e-mail address for a domain. This may, or may not, be the same as the customer's own e-mail address. And there are at least 3 contacts per domain (Admin role, Tech role, and Registrant).
If for some reason the verification e-mail is not received, or not acted upon, ICANN will disable the domain by taking over the registration, temporarily transferring it to name-services.com (through eNom, a Dreamhost partner). The unfortunate side-effect of this can be a Dreamhost customer is unaware their domain has been disabled, as the ICANN action disables all and any services, including DNS. If any domain so disabled was to provide e-mail services for one or more contacts on said domain (or another domain), verification becomes impossible.
I'm suggesting that Dreamhost add a feature that when this happens, or is about to happen, notifications are sent to the Dreamhost customer via the same contact methods used for notices such as support requests, billing, announcements, etc. While this may not always work, it can perhaps reduce downtime for DH customers. This would be especially beneficial for those Dreamhost customers who have their own clients to service on Dreamhost.
A simple way to do this would be follow-up e-mails sent a week or so after the registration change. I don't know if Dreamhost would be able to further automate this, such as detecting when a customer-hosted domain is taken down for ICANN verification.