That these problems are DNS-based. Given that there is someone with motive, I'd say that DNS poisoning is going on.
Hmm.
But that doesn't sit right with being unceremoniously hoofed off II, tho. So it's not DNS. Temporarily broken DNS would make re-connecting difficult, but wouldn't affect existing telnet sessions.
I stand by my assertion of SOMETHING, and I'll let you know what I know what the something is :-)
If there's a DOS attack in progress (and I'm not convinced there is - a horked up router configuration with routers bouncing crappy info to each other via RIP or OSPF could produce effects like this) then the attacker is likely generating spoofed packets along the way. But the periodicity of the outage smells of routers to me.