I mean, bitcoin-qt does a lot of disk IO during blockchain synchronization. Maybe your OS ends up doing lots of swap too and it stops accepting new TCP connections because it is not managing to handle it? I don't know, just trying to guess.
Maybe the best way to test would be using a SDD. Or with the blockchain in a different disk than the rest of your system, including swap.
I'm on a Core i7 with dual SSD's and 24GB of RAM.
But I don't think that would be it anyway. When it goes down, the entire mesh network goes down. I am connected to the Mesh Gateway router so I think I'm taking that down with Bitcoin. When that does down, none of the other mesh routers can talk to the gateway.
At the same time, a computer connected to the dsl directly pings out fine.