servermojo.com looks like it may be a possibility, site24x7.com isn't free for dns monitoring.
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Hmm. Apparently not -- it just monitors http and https.
Well actually it does, indirectly.
The testing process includes dns resolution. If the test fails at the point of dns resolution, the alert will show that. The alert actually shows at which stage of a complete test pass a failure occurs. We even clock the time for each stage, we just don't show it in the reports.
But it looks like basicstate.com will do what I want. Why didn't you say so?
The rules here don't allow it. But, once you have broached a subject, clarifications are allowed.
I can't point you to the exact rule numbers, but that is my understanding.