Clay, without any info on the exact make/model of system, here's all I can theorize from what I know in general about these systems.

Most all these systems tend to use the "unlicensed, low-power" bands allocated for such things as remote controls, baby monitors, cheap R/C cars, etc, etc. There are several unlicensed low-power device bands in the VHF and UHF spectrum -- 433 MHz, 900, 915 Mhz, 2.4Ghz, etc.

These bands are used by a wide variety of consumer electronic devices. Without knowing what kind of modulation/encoding your car remote is using, all I can guess is that some other wireless device is causing enough interference to make the car's receiver go into the start sequence. This, sadly, is a really common problem with the unlicensed, low-power spectrum; devices interfering with each other or blocking each other's signals.