Up to line 23 the date is 1 Jan, then it switches over to 22 Nov. I expect this is normal and happens when the clock synchronizes with some NTP server. What I find confusing in this log is that certain services, e.g. upnp, pppd, and some processes, keep stopping and starting in quick succession. Within 2 minutes you have obtained two different IP addresses from the ISP, the VPN modules were unloaded twice and so on. Unless you are doing this your self, e.g. by resetting the PPPoE connection, then there is something clearly amiss with the router. It may be the hardware or it may be the firmware. In any case, this is not the expected behaviour of a router. To follow a process of elimination borrow another router from a friend, configure it with PPPoE authentication for your ISP's settings and see if the problem persists. The fact that your PC's PPPoE client does not experience disconnections or similar problems, points to a suspect router.
As I don't have in my possession a modem or router like yours, I'm not sure I can help further with this problem. I hope you find out what's wrong with it, but I suspect that you may have to replace the device altogether.