I've found that the safest place to fly a 27 MHz AM plane is out in the middle of nowhere. I know that Citizens band radio is from 26.965 MHz to 27.405MHz, but you'll find it more common for most CBers to have radios that will go up to and past 27.455. Generally, those channels are used for SSB (sideband) but there are some that will talk AM on those channels. The older RCI 2950's could be jumpered out to go from 26.000 to 40.000 MHz. Normally, the radio is tuned on channel 20 (in the middle of the band). The bad thing is that the farther away you get from channel 20, the less effective the antenna becomes. While it's not too noticible on sideband (because there's no carrier signal or dead key), AM modulation tends to splatter. It's even worse on a mobile unit because there's no earth ground to help absorb the splatter.
This might not be what is happening in your case, just something to watch for.