I've been having this issue intermittently since watchOS 3 & iOS10.
It's been more often the past couple of weeks. I did a completely fresh install of iOS10 on my "new" iPhone 6 (warranty swap) the first week iOS 10 came out (September?).
I also have an iPad & iMac, both set up to receive my iMessages and SMS-to-iMessage (or whatever they call it) And all set up with AT&T Number Sync (shouldn't affect iMessages or SMS). The iMac is usually off.
I often watch Podcasts on my iPad while working on my winPC, with my iPhone on the desk, and AW on my wrist.
Usually, I would get drop-down notifications on my iPad, and nothing on the others, but not want to reach over my PC keyboard to reply, or miss a notification when I'm not looking at the screen, so I usually put it on Do Not Disturb. After then however, I will NOT get a Notification AT ALL on my watch, even if I swipe down to the Notification Center. And No sound or screen light up on my iPhone, but then when I wake up my phone for whatever reason, the notification(s) is on the lock screen, sometimes. Sometimes there's no notification on the lock screen, but there will be a Badge Number on the Messages icon.
Too many times I have missed messages from my coworkers or my wife. Simply infuriating. Thanks, Apple, for making feel like a dip$h!t for wasting thousands of dollars on your garbage that doesn't do the #1 thing I need them to do - communications.
It's been happening more often, with or without the iPad in DND. And in both of these situations, I'm home with excellent Wi-Fi signal (2 Luxul AC WAPs with a wireless controller) and full LTE signal (tower outside the neighborhood). I don't go out to job-sites every day, but today it seemed to be working fine when the iPhone & iPad had 1-2 bars of LTE. I got about a dozen messages when my hands were full within 5 minutes. I surely noticed those!
And, yeah, I've tired the Notification settings shuffle for the AW & iPhone, and all the other crap. Everything except fresh restores. I refuse. Rebooting the AW, iPhone & iPad usually works for a while, as others have mentioned, but it's usually doing it again by the next day. I'll test & confirm by sending myself messages from my wife's iPhone, before & after the reboots.
My wife suggested a visit to one of the 4 Apple Stores in town. I might, but I have a feeling their only suggestion will be "restore everything from scratch" FFFFFFF that!!! I'm so sick of these productivity stopping problems, and their lack of solutions. This kind of stuff happens far too often. For a while I wouldn't receive phone calls, back in the iPhone 5 & 5s days. I have to change my voicemail message to "My phone didn't ring, leave a message and I'll call you back." I just changed it the other month.
But hey, we can send balloons & confetti in messages... so wooptydoo... At least we know what Apple's priorities are.
Watch Sport 42mm "Series 0". iPhone 6, AT&T. iPad Pro 12.9", AT&T LTE. iMac Retina 5K, 27-inch, Late 2014, i5. All up to date on public releases, as of day of update release.