For those still interested in this topic I've pretty much confirmed my suspicion regarding the output jack of the Fender Dimension bass, and the failure of the Relay transmitter to remain seated properly.
At this point, I've simply rigged up a 12" adapter cable. The female end is strapped to the guitar strap, and the male end is a 90 degree plug, so it's rather low profile and elegant. When it's gig time I just plug the transmitter into the adapter cable on the strap and it stays locked in exactly as it should.
On another note, I had the unit less than 1 week and got this problem solved in time for a gig on Saturday. I discovered on Friday evening that the transmitter would no longer charge! So I clearly had a defective unit. On the way to my gig I swung by Guitar Center to return it and fortunately they had another in stock, and I was able to do a straight across swap. I had time to charge it before the gig and used it. All went well! After that experience, though, I am concerned about the longevity of the transmitter battery and/or the quality of the components. We will see.