> I'm currently looking for a job, but due to extensive and exigent family matters, I've not really had the time or focus on requests by hiring managers, or really follow up on leads. Worse, I don't know when it will be resolved enough to allow me to focus again on the job hunt.

Either you are looking for a job or you aren't. 

If you are looking for a job, then you are ready, willing and able to go through every follow up step to get interviews and take up the job if offered and you like the offer enough to take it.

If you re not looking for a job, then you need not do anything.

What you cannot do is say that you are looking for a job and follow up with "I have an exigent family matter" every time someone wants to discuss the next step with you. Whether you go into more clarifications with your exigent family matter is immaterial. The message that your recruiters get and work with is that you are not available. Period. And your recruiters will react by working with someone else - they make money by recruiting. If you are not available, you cannot be recruited. If you cannot be recruited, then they can't make money from recruiting you.

Once you've taken care of your family matter, let them know that you are available. Or they'll contact you again on their own three to six months from now and ask you you're doing. Recruiters will work with you as long as they think they have a good chance of making money. They'll drop you like a bad habit if they conclude that you are not someone they can introduce to their clients with any good chance of success.