I don't remember the exact error text, but it's a 500.13.
Which is the maximum concurrent connections. We're configured for unlimited.
The troubleshooting process is kinda like the wheels on the bus. Round and round.
We've ruled out it really exceeding any self-imposed or internal connection limit because it can do the same thing (shut down ASP and start throwing 500.13's, which happens AFTER ASP shuts down) on very low traffic.