Unbearable disconnects

I was showing a new player around and continuously getting disconnected from the core Tyrian maps. The worst is Black Citadel. I've counted three disconnections, and I always end up in Lion's Arch. As I write this I can't even connect to BC. I performed a speed test, and it reports 100 Mbps both ways, so I know things are fine on my side. What's going on? These performance issues are embarrassing and not a great first impression for new players.

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