The radio controlled clocks are looking for a signal on a very low frequency, 60KHz. Noise from the sun (literally) makes reception on this frequency very difficult for cheap receivers with small antennas during the day. The signal these clocks need is only transmitted at the "top" of the hour. And running the receiver is very consumptive of the battery. As a result, these clocks generally make four attempts to receive the signal per day. Attempt number one starts at 10:55PM and runs until 11:05PM. If it don't get the signal on that attempt, the clock shuts its receiver off until 11:55PM and runs until 12:05AM. If that fails, the clock will try again from 12:55AM to 1:05AM and then again from 1:55AM to 2:05AM. So, first you have to set the clock to within about +/-three minutes of the correct minutes after the hour. Then, if you do need to reposition the clock, you'll need to do it late at night or very early in the morning.
By the way, when we did the fall back thing last fall, it cost me a new dishwasher! "What," you may ask, "Some sort of Y2K bug or something?" No. I climbed up onto the kitchen counter to set the clock above the kitchen sink. Being near the sink and having a tile top, the counter was wet and slippery and I fell backwards to the floor. Sort of puts a whole new meaning on "fall back." On the way down, my feet hit the dishwasher door and broke it right off its hinges. I was black-and-blue down my whole left side for weeks. And the clock over the kitchen sink? Well, as of Sunday morning, it was finally back on the correct time.