Why does XMLHTTPRequests from IE 10/11 fail intermittently against F5 LTM+APM?

Could you clarify a few things?

we see that IE sends the request headers, the VS sends an ACK followed immediately by an ACK/RST before the client sends the POST body.

Does the XHR client send a single HTTP POST request? And if so do you see a full 3-way TCP handshake, and then the HTTP request headers? Is the POST payload not in that first HTTP request?

It turns out to be precluded as a workaround for us because most of this team’s endpoints need to be accessed by both a user’s browser (where an APM session can be expected to be active) and by other application servers (which will not have an APM session)

So you're saying some requests will be coming from agents that haven't authenticated through the access policy? When the XHR requests happen, do you always see an MRHSession cookie in that request? If XHR agents are accessing the APM VIP without an initial browser session, have you made allowances for those agents to handle the initial 302 redirect to /my.policy?