Have you already read through the existing threads in this forum about high CPU usage? Did any of those sound similar?
First, embarrassment. I had searched with my router model and found nothing that matched well.
So I just searched "snbforums high cpu" and found an overwhelming number of hits. Now my embarrassment has turned to anger.
Several responses suggested turning the router off, keeping it off for a while, and turning it back on. While not helping in diagnosis, that works for my problem. I already knew that worked; I've done it twice now. But I was looking for something a bit less disruptive.
Some were appropriate for high cpu following firmware upgrade and, if I understood correctly, involved resetting to factory settings. Well, I had done that both before and after upgrading from the out-of-the-box ASUS firmware to Merlin 384.14_2 about 2 weeks ago. (If a procedure that clears all user settings is considered an appropriate procedure by ASUS for a consumer grade product then I think I have the wrong brand of hardware.) But I've made no such changes for 2 weeks. I've made lots of config changes - turning on VPN support, turning on DDNS support, etc., but now firmware upgrades.
Some suggested clearing nvram as a solution to high cpu. If that is equivalent to resetting to factory settings I've already expressed my opinion of that. I'll continue powering the router down for a few minutes instead. That, at least causes a lot less downtime than needing to reconfigure the router.
Login with SSH and run this command when you see CPU maxed out:
This should show the top 20 processes using CPU. Run it a few times and post the results that seem the most representative from one run to the next.
Since I'm not having the problem at the moment, performing this is obviously not showing much useful ... except to show me what normal activity looks like. But I'll save this command and issue it if/when I'm hit with the high cpu condition again and see what it shows.