As a DP/Director/Editor/Human I've learned a couple things about sound guys that I think will help you (and your sound guy) out. Here's one of the things that I've been doing recently and it's making life easier for everyone:
Hire a soccer ref to record your sound.
Ok, he doesn't have to be an actual ref, but he should have a yellow card and a red card. He probably won't own a pair of penalty cards, so be a nice guy/gal and let him borrow yours before the shoot. They cost like ten bucks on Amazon and they'll last forever. They also come in handy if you and your crew play a friendly during lunch break. If you're in a pinch you can use colored note cards, but legit yellow/red cards would be way cooler.
Here's how I like to use them:
When we're setting up to film an interview I have my sound guy (in this example the esteemed TJ Hill, yes THE TJ Hill) sit somewhere in my line of sight that's off camera. If sometime during the interview he runs into an issue that's not an emergency, but it's something that needs to be addressed as soon as possible (ie. his batteries are running low, a cable came loose and is making a noise every couple of minutes, the talent keeps moving every minute or so and it's rustling the lav) he gets my attention with his yellow card.
This allows me - the director - to make the decision on how to proceed. I can listen to what the person is saying and decide on the easiest, most natural way to find a stopping point where we can fix the problem. Since this is only a yellow card, I'm not going freak out and interrupt the person if they are talking at that point. I'll let them finish what they're saying and then at the next natural pause say something like "You're doing great, let's take a quick water break" and then I'll take a sip of my water so the interviewee thinks that I might be the one that needed the water break and then they feel free to take a sip of the water that you placed near them (you remembered to do that right?). During this quick break the sound guy can now fix the issue without the person even knowing if it's a simple battery or cable issue or if they need to adjust the lav on the person it at least doesn't feel like an interruption and they won't suspect that something went wrong. After the quick break, we can transition right back into the interview.
The key is to NEVER draw attention to a technical error. The interview subject doesn't need to know about it and the only outcome to telling them what went wrong is that they'll lose a little trust in you, they'll wander if what they just finished saying was usable, and will start to wonder if the gear is working instead of focusing on their story.
If something mission critical happens during the interview and we've either stopped capturing audio or the audio is completely unusable, that's when the sound guy raises the red card.
This lets me know that nothing the person is saying right now is usable and we have to fix it ASAP.
Now, I've seen several sound guys (and producers) at this point interrupt the person and make an announcement to everyone that the battery died (or whatever the problem is). This is the last thing you want to do.
Instead, when I see the red card I pay close attention to what the person is saying. Again, if it's something that's not important to the story I'll let them finish their point and then say the let's take a water break thing. If it's right in the middle of the most important part of the story, or they're getting super emotional I let them ride that out, too. I try to never interrupt the person I'm interviewing, even in a situation like this. At this point you might think I'm crazy, but I've found that it's better to let someone process what they're going through instead of interrupting them. At best, you have a second, lesser quality audio source like the built in mic on your camera that could be used in a pinch for a few seconds in the edit, or at worst, you're going to lose that moment anyways, so you might as well do your best to keep them in a good place mentally and emotionally.
If the critical error is something like a battery died or something, the audio guy might be able to fix the problem quietly and start rolling again without anyone but you knowing. If that's the case you can then ask a follow up question and keep going like nothing ever happened. If it's not something you can take care of seamlessly, wait for a good opportunity to have a water break, fix the problem, and pick right back up. If you're lucky you may be able find a creative way of asking the person you're interviewing a similar question later in the interview when they're back into the groove of things.
Whatever you do, the main take away of the referee routine is that you establish a clear method of communication with your sound guy (or whole crew for that matter) to ensure that no one on set interrupts the shoot and to give the director the information he/she needs to make the delicate decision of how to stop and how to move forward.