Just a guess but looking at your LOG3.txt file I would think the following lines are relevant:
Jan 15 12:17:44 kernel: eth0 (Int switch port: 3) (Logical Port: 3) Link DOWN.
..
Jan 15 12:17:45 WAN Connection: ISP's DHCP did not function properly.
..
Jan 15 12:17:47 kernel: eth0 (Int switch port: 3) (Logical Port: 3) Link UP 1000 mbps full duplex
Jan 15 12:17:50 WAN Connection: WAN(0) link up.
It looks like the firmware has reported appropriately that eth0 (WAN port connected to the internal switch port 3) is DOWN.
Then a few seconds later it is found again and connection re-established.
Intermittent connection problems can be a struggle but you must be methodical in debugging them. I generally work from solutions that are quick and easy to check to the more demanding ones if necessary.
So I hope you (and others) can bear the pain of the obvious. I don't think you can easily dismiss hardware issues as they don't always show up immediately, nor can you dismiss software at this point.
- The usual tech support advice: Turn off your ISP's modem/router and your own router. Unplug and reconnect all cables (with appropriate delays for capacitors to discharge) for the WAN connection - fibre/coax/twisted-pair through to the ethernet cabling to your own router. Re-power ISP and check status lights for connection, then re-power your own router and check status lights;
- WAN connection (to ISP router/modem device) cable connection: you can replace/test the cable and RJ45 sockets on both ends; Once I even had a powerbrick's power cable running almost perpendicular to an ethernet cable which showed intermittent disconnections until I moved the power cable - this should be a relatively rare event with modern cables however;
- Internal heat within the router causing problems with some board components: You can almost never rule this possibility out, although you can certainly reduce the software load on the router (by temporarily shutting down optional services), make sure there is optimum airflow around it (it's not right next to a heater?!), cooling vents are unobstructed, etc.. Internal diagnostic/performance indicators should help determine if this is a problem. An IR thermal camera might find a "hotspot" inside your router's electronics. Sometimes an external fan can be used in an attempt to increase airflow/cooling across the router.
- ISP Modem/Router logs: I haven't had a great deal of success with ISP device logs over the past 20 years or so - typically they are underwhelming and don't provide much, if any diagnostic information. If you are lucky and have a customer login to the device you might find a reconnect type message corresponding with the date & time of your own routers reconnection. I'm not sure you can rule out the possibility of a disconnection on the ISP's equipment end yet. It's also possible that the ISP updates their own firmware from time to time and sometimes it doesn't always go well with the connected world. This, of course, is much harder to diagnose without ISP equipment logs, but you might have some success with the ISP's higher level tech support, or not!
All the above process will take a little time and should be part of a generic protocol for reconnecting your own LAN and Router to the outside world via the ISP's equipment. There is one final part of the log3 content that I might speculate upon and might only be relevant to your unique problem - the DHCP conversation between Router and ISP which has been flagged in the log. This might be a concern as you cannot determine which side of the conversation might be at fault - you cannot, for example, reload firmware for the ISP device without their tech support intervention. You certainly can re-flash your own firmware as bit-shifting of ROM contents is still a technical possibility. All the Asus routers firmware update protocols should be followed, remembering to save your existing settings and re-set to default after a successful firmware flash before reloading your "old" settings. All routers are built to a price and very few have adequate cooling for the long-haul, especially when lots of services are running all the time in a heated room. There are a few hacks, adding a 5V fan to the case around the web, which others have found necessary. You don't always have to go this far however!
I haven't looked at anything malicious at this point, even though you can't rule it out completely. It's just quite a bit harder to diagnose, especially if the breach is on the ISP's equipment side. Plug-n-Play services, for example, have been regarded as a security hazard for some time now. I'm assuming you're using your router for some media delivery services, which is why your logs are showing it's enabled.
Anyway, I hope this helps anyone out there. It would be nice if your router showed more problems and pointed to other issues as well. My own guess is with the ISP's equipment and/or connection...
Best regards
Dave