TLDR: If RTC is unable to contact your Jenkins 1.584 server, try downgrading to Jenkins 1.574.

This forum was one of the places I looked for a solution to a problem I was having, so I thought I'd share my findings here. (I'm using the 4.0.3 RTC Client.)

I'm using the Team Concert Plugin on Jenkins in order to allow the Jenkins servers to act as RTC build engines. I have 7 different Jenkins servers and I've found the following problem to be true on multiple (though not all) machines. 

I upgraded from Jenkins 1.574 to 1.584. While doing this I also updated the Team Concert Plugin from 1.1.8 to 1.1.9. Shortly after doing so, I began to (sporadically) see the following symptoms:
1 - On the Hudson/Jenkins tab for the buildengine, the results of running Test Connection would be : "Exception: No Hudson/Jenkins header found! Test connection FAILED!"
2 - The Get Jobs action on the Hudson/Jenkins tab of the Build definition would return no jobs.

On the Jenkins side, I was always able to verify that the RTC build definitions existed, so no problem was evident for that direction at any time (even during those times that the reverse direction was problematic). 

The problem was not consistently present across machines (there are some that have not yet seen it), nor was it consistently present on a particular machine. The most problematic machine would work immediately after a Jenkins restart but would begin to fail shortly afterward - even though my only actions were Test Connection (pass), wait a few seconds,Test Connection (fail).

It would be nice if I'd employed some Scientific Method here and in one group I moved back to Team Concert Plugin 1.1.8, in another group I moved back to Jenkins 1.574, and in the third group I stayed at 1.1.9/1.584 and then did statistical analysis. But no, I moved the first machine back to 1.574, that worked, and then any other machine (two others so far) that exhibited the problem I'd revert to 1.574. It hasn't failed me yet.