Even as a small company we have a number of regular infrastructure reviews. Most of the time we just go through the review, find nothing has changed unexpectedly and no new ideas need bringing to the table, we sign off to say all looks well, and the prices takes very little time. Some of this is automated: scripts collate and report information for signoff and we humans verify the result and take actions as needed (in some cases the action needed is to update the script(s)). This may seem wasteful, but a couple of people spending a couple of hours total per month on such checks can save some nasty surprises in future.
Domain status checks is one of the things that gets reviewed.
Has the advantage that a failure might not be so disastrous either.
Also, get a registrar with an API and use a script to figure out how long a domain is valid. Alarm through your monitoring system when you hit the too close for comfort time frame.
You can scrape whois as well but that seems fragile.