... It will operate down to 1.1, but when the voltage gets to 1.3, the receiver drifts, and I have to constantly adjust the tuning capacitor to receive the signal. It gets more and more frequent until I give up and change the batteries in frustration.
Have you measured the battery voltage whilst the batteries are in the device?
Yes, it's ideal to work down to 0.8V per cell but it's not always possible. Suppose the device uses two AA cells and a PIC microcontroller which is only guaranteed to work down to 2V, it might work down to 1.8V but the chances are it won't.
When I design, I aim for 0.8V per cell and will settle for 1V per cell but I wouldn't consider 1.1V per cell.
Right now, with the device off, the cells are at 1.30 volts (Fluke 87-3, standard mode) WIth the device on, the cells are at 1.26. It's operating fine now, but when it starts to drift, I'll measure the voltage, and then continue to measure it as it gets worse, up to the point when it becomes too irritating to use. The numbers in my earlier post were from memory - I check the voltage of the cells when I replace them.
I'm not an RF guy, so I don't know what trade-offs had to be made in terms of cost, size (fit into headphones), etc. etc.