CPU dropping to zero would seem to be an anomaly IMO. If the server is flooding with connections, I would expect the CPU usage to go very high as the software tries to handle the extreme load.
I wonder if you could be having a CPU problem, maybe overheating? that is causing the CPU to shut down. Just a guess, but the zero CPU is an important clue IMO.
Suggestion: run this stuff by Jon Tara on SI. He is pretty sharp on this stuff. Dream Machine thread.
I'd want a program running to tell me where the connection load is coming from, especially at the burst. If it's not a DOS attack, then is it a hardware issue or a software issue? Or something from the isp?