It turns out, that neither had ever made the phone call to ask.
Often, in the job search, it's easy and more comfortable to get into a routine, to learn how to use a certain strategy and repeat it over and over again. Yet, if a certain approach isn't producing results, you need to change your approach. Try something new, and see what happens, even though it probably will feel uncomfortable.
If you're not sure what to do differently, ask. The most effective tool for asking is speaking with someone, either in person or by telephone. Compared to e-mail or a formal application, a phone call is more personal, often takes less time, and provides more candid information.
You may feel as though you are irritatingly intruding into someone's work if you call. Or, you may feel that you will offend the person with a phone call. Or, you may feel that people will be very polite and not provide you with information. Or, you may have another reason.
All of these are true some of the time, but I would bet that it's not true most of the time. And, if your other strategies aren't producing results, then the worst-case scenario is that you end up in the same place as you are now. The best case is that you end up getting a job. In the middle, you may find some new job leads or some information to help you in your search.
If you feel safer, you can also only contact those companies who have rejected your application, or that you haven't heard back from in more than three weeks. That way, you have even less to lose.