It's possible that this domain's ads ran only on highly-niched phrases or product-based keywords that we don't currently search.
Another thing to consider is restrictions on the ad: Google gives advertisers some budget-saving options that keep their ads running only in local areas or during certain times of day. Or they have budget caps, and we looked for the ad after they hit their max. We might have missed seeing their ads because of those settings.
You can try adding the domain's paid keywords to our list of keywords to search. It helps increase the chances that we spot them next time.
We collect data from the first 100 SERP results on every keyword we search. If the domain isn't showing up, it might be ranking lower or ranking for highly-niched keywords we don't yet search. However, with millions of keywords in our database and 100 results for every one of those, not seeing any rankings for a legitimate domain is rare. Double check that you've spelled the entry correctly. Leave off any https and www, and make sure that the top level domain is correct. (.net vs .com, for example)