Okay, I have found the problem. I cannot explain why and I feel a litlte stupid about it, but I had to have been mistaken about the refer working fine before. There is no way that the refer could have ever worked correctly on the inverter.
We usually take an old orange juice jar, fill it with water, and freeze it. Then a day before we are to leave, I'll place it in the freezer when I turn everything on for the pre-trip inspection.... Apparently, that ice has kept everything cooled off while we traveled to/from campgrounds and home.
Here's what I found; First, I believe during construction, the slide assembly is prebuilt and prewired. When they set it into the frame, there are three odd looking electrical connectors that are plugged in when the slide is put in place. What happened is that two of those plugs were inadvertantly swapped, so that the inverter was powering up two receptacles on the slide, and the refer was simply connected to a breaker in the panel.
After I rung out the wiring and drew a schematic, it was obvious what was happening. So I swapped those two weird plugs and everything seems to be working right.
I was more than a little disappointed in myself for not catching this months ago. We've had the unit since July, '15. However, it stayed at the deer camp for almost two months, and we only took several weekend trips during that time, but they were all short trips.
Anyway, I think all is well now.
Thanks for all the input guys,...you helped more than you know.
2016 Ford F-350 Lariat CC, 4x4 SRW. B&W turnover with extender. 2015 CC Silverback 29RE, fitted with Reese Goose Box. Amateur Extra Class K5TS, 2016 nights camped 16