Meh. My mission-critical devices get rebooted for kernel/daemon updates, the occasional power outage, and nothing else. I do not tolerate critical gear that can't handle that.
(Admittedly, that rule still leads to periodic reboots, but not once a week or anything like that. Once a quarter is typical.)
Not saying everyone should reboot everything daily or weekly. Just saying holding on to Alpha firmware or potentially suffering performance impacts is not worth trying to set some meaningless record. Plus, these Asus routers are not exactly highly refined mission critical devices. Just knowing my Asus router had been up and running for a month would be enough for me to reboot it, they aren't known for flawless memory management etc, and who knows what impact that is having at that point.
If your devices are truly mission critical you should have them in pairs which allows you to do maintenance without any impact. I would not have considered my previous setup "mission critical" and I wasn't going to spend a ton on dual of everything, but since it ran email and web servers for myself and various friends, and a lot of network monitoring and other stuff, I would do maintenance at like 3AM. A big UPS and very reliable power made that minimal concern (only once did I have to fire up the generator during a 3 or 4 hour outage). All enterprise network gear which I got dirt cheap or free and a pretty decent (albeit not terribly high end) Dell server.
If we want to talk about records, I've lost track of uptime on various Cisco gear I've worked with. Just took down a pair of 7304s that were at 11 years of pretty heavy use, typically pushing around a gig of unicast and multicast all day 5 days a week, and large synch jobs over the weekend. That may be my record but I want to say I've seen a forgotten router that was at more like 15 (end of life, end of support, not doing anything other than wasting power). In my previous job we had a pair of 7500 core routers that were in 1 WFC (next to the WTC towers), after 9/11 we watched the temperature creep up gradually over several days to well beyond critical, and weren't able to determine if the generator ran out of fuel or the routers thermally destructed. Only one circuit was still up (second router was reachable via the first, not directly) and everything went down at once so hard to say. When we finally got in there to recover them they were packed solid with concrete dust. I believe someone told me they did power back on but nobody ever hooked them up to see if they were booting, they were considered hazardous waste at that point. In reality the only reason I've not seen ones at 20 or 30 years is simply equipment life/support cycle requiring it to be replaced. Of course a low end 1941 type router may not fare as well, but that's what I used at home and I know it ran for over a year at least once.
When you find a good, stable IOS, Cisco routers can run virtually forever as long as they have power and some amount of cooling. Just don't turn them off after 10 or 15 years and expect all the fans to spin back up when you turn them back on (if they turn on at all, sometimes that is also certain death for the power supplies).
Now my home stuff gets rebooted at least every couple weeks. That includes fire stick, that thing has awful memory leaks