Need a little help with a shitty website

So, I spent most of the day troubleshooting a website that drastically slows down when 'a browser looks at it funny'...

Usually it behaves fine - it's not the volume of requests, my teammates think it's something about the kind of requests. But they're struggling to get the logging properly configured.

I'm an EUC engineer (p.o.s. website requires IE11 and ActiveX controls - yay healthcare!), so mostly helping on the sidelines, but I'm looking for some 'supportive' suggestions...