Just to close the loop on this, and to help out any future owners with similar Sirius reception issues, my problem is now resolved.

The dealer installed an external antenna on my 2007 Camry Hybrid. The antenna was originally designed for a 2005 Land Cruiser. It fit the receiver that came with the OEM Sirius Fit Kit that the dealer installed prior to my taking delivery. Toyota's instructions call for the dealer to place the antenna on the inside of the windshield, behind the rear view mirror, in the shade/pattern of dots. That placement was undoubtedly the cause of my frequent, unexplained drop outs in reception.

Now that the external antenna is connected, the reception problems are 99% gone. Last night and this morning I drove the same areas in which I'd been having problems, and there were almost no drop outs. The drop outs I did experience were shorter and less noticeable, and within my personal level of acceptability.

Bottom line: the internal antenna, at least when placed in the sunshade area of the windshield, presents unacceptable difficulty with reception. The fix for me was an external antenna.

Cosmetically, I'm not completely satisfied. The dealer put the antenna on the trunk lid, which is fine (if you want good reception, it has to go outside somewhere!), but it isn't centered. They stuck it off to the passenger side of the trunk. It might be that they didn't have enough cable to put it in the center, but I don't love the way it looks. Also, the dealer left the offending interior antenna right where it was installed. Common sense would have dictated removing it, in my view, but I guess I can live with it. If the dealer was closer to home, I'd have them fix it.

Thanks to everyone who chimed in with their comments in this thread.