As the title says, I have an ASUS AC3100 router, was close to top-of-the-line back when I bought it.  In the last few months, it will randomly disconnect devices, either wifi or devices connected by CAT5/6 cable.  

Firmware is up to date.

Resetting the router (power down and back up) will reconnect the phone or computer or whatever was disconnected, often at the expense of some other device getting disconnected.

Connected to the RG45 jacks on the back are several devices like the NVR and roku, in fact the rear connections are almost completely full.  The wifi services several cell phones, laptops, and tablets (not all in use at the same time but if they're powered on they're connected).

I don't find this problem reported in the same way anywhere else, ASUS has a troubleshooting page for the router dropping wifi connections only.  

So, is it time for a new router?  They still sell this one so it can't be obsolete, and anything else I've looked at doesn't support as many wired connections as I use now.

Anything related to the devices being disconnected?

Check DHCP pool, maybe not enough leases?

What do the logs say?
Check your DHCP pool size and utilization

You can extend the life of Asus routers by putting them on a laptop cooling pad plugged into the USB port.  Heat tends to kill these things pretty quickly as they have no active cooling.  Usually they will start to become unreliable as you are experiencing before they totally fail.

You can do a factory reset and update to the latest firmware which could help rule out hardware failure.

I find about 3 years of operation without active cooling is about what you can expect from these things before reliability degrades. With a fan under them they last much longer.

There's also the possibility it has been damaged by a power surge either from AC power or a network line.

If it can't handle wired or wireless I'd just outright replace it.

Leases? Most home routers have a /24 for internal devices so  ~ 250 devices.  If it isn't letting go of them back into the pool it is malfunctioning or OP has the town bicycle wifi network.

Firmware may be corrupted.

Might be time to invest in Unifi devices. Get a UI dream machine pro SE. I got the pro version, get the SE version. Add in an access point and you will be set.

https://store.ui.com/us/en/pro/category/all-unifi-cloud-gateways/products/udm-se
https://store.ui.com/us/en/pro/category/all-wifi/products/u6-pro

You can go for wifi 7 if your devices support it.

Thanks for all the replies and suggestions!  

I attacked it again last night.

The router was telling me it wanted a firmware update, so I'm guessing the one they sent out in December screwed up something and they got enough complaints to fix it - just my theory because I don't think routers update their firmware this often.  So I updated the firmware ... or did I?  It is still saying it wants to update even after it updated...  

I was not able to get internet wirelessly on my laptop anymore, it only worked through the cat6 cable.  The laptop is connecting to the router through the wifi just fine, but there's no internet getting through.

I have a wifi scanner app on my phone and noticed the 2.4ghz signal wasn't even showing, and my 5ghz one had dropped the SSID name.  Fiddled around trying to figure that out, then decided it was time for the big gun, factory reset.

Did the back-to-scratch factory reset, renamed the SSID, got the household devices to match the new SSID and encryption word, and so far everything is connected and happy.

Wife wanted to go postal on the HP printer (I have a longstanding hatred for that thing) because it's impossible to change the network settings - the HP app shows it offline because the network settings are wrong, and there's no way to get it to come online so you can change them.  I finally disconnected my laptop from the shore power and connected to the printer directly with a USB cord, which then showed two of the same printers, one offline and the new one online.  Changed the network settings in the one I could and suddenly the printer came alive.

As of this morning everything is working properly!  

Id go with what @GraboidHunter said about the cooling pad, also ditch the asus firmware its generally crap and pretty limited in what it can do.  if you are more than a general computer user and can figure stuff out id go with running DD-WRT on it and you basically upgraded your router to something more akin to a business class router.