http profile on layer 4 server intermittently breaks connections

It is very likely that someone changed something regarding the HTTP profile, otherwise this should not have had an impact. In Fastl4 the http profile only supports statistic collection. Any attempts to modify the http stream, such as by insertion of a header or an irule, will fail. You can read more about that here:

https://support.f5.com/csp/article/K16446

If you need a better root cause, I would open a support case. Be aware that they are going to need to see the failing traffic capture to give you any meaningful feedback.