Found the problem. Since Apache v2.3.6, FcgidMaxRequestLen is defaulted to 131072 bytes, prior to that it defaulted to 1GB.
Any attempt to send an HTTP request bigger than 131072 bytes causes a 500 Internal Server Error.
apache.conf doesn’t show any entry for FcgidMaxRequestLen, so it’s deault value is hidden. I had to add one. I’ve set it to 25MB for now which is the same as the max email attachment size.