Is that an Apache error? Is it the exact error text? Nothing came up for it on a google search. Is it a custom error page? What HTTP response code is logged on Apache?
The major changes that would potentially happen when you introduce the BIG-IP to the connection path are source address translation due to SNAT'ing and/or server side connection re-use due to OneConnect. It doesn't sound at all like a OneConnect issue. Are you using SNAT on the BIG-IP VIP? If so you might try disabling this to see if the error goes away. I'm guessing not, but it's worth a shot. Can you change the default gateway on the Apache servers to the BIG-IP and disable SNAT? Does the request then work?
Aaron