In the vicinity of high voltage transmission lines, and if you are that near the plant, the lines are probably at least 345,000 volts. These lines have significant electric field associated with them, and can induce substantial voltages in metal objects around them. Basically if you apply enough voltage at the antenna terminal, bad things are going to happen. Be thankful your radio actually still works!
My guess is that your radio is suffering from an forced hard reset. Basically the induced voltages are high enough to cause bad things to happen inside the radio. It might be possible to design a high pass filter to go between the antenna cable and the radio. A 'trap' would be better, but a trap resonant at 60hz is going to require large and heavy components.
You basically have a device designed to detect signals that are quite literally microvolts, being subjected to tens of volts.
Never underestimate the ability of very strong electric fields ability to wreak havoc on electronics. In my University Days, the Department of Electrical Engineering was located about 500 yards from the Computer Center. For one week each Semester they operated a search radar. The mainframe at the computer center would often crash 10 times a day during that week.