Nevermind, I figured out the problem.
FYI for others:
This was due to a delay in Apache in my WAMPSERVER setup. I had "Require valid user" enabled for the mod_auth_sspi module. Evidently there is a delay while this module verifies the logged in user (NTLM) against AD, and until the user is validated all post data is ignored.
I disabled "Require valid user" and the problem went away.