It doesn't matter if there are actually humans awake to report what is happening. Every spaceship transmits some kind of signal to its ground control. It's been that way since Sputnik. You want exact coordinates of your ship at all times, and with the near-future tech you're talking about the spaceship would undoubtably be transmitting status reports every second of the day. It doesn't matter if humans are awake to transmit them, that would be redundant.
You're right, it is hard to find a believeable way to do this, although equipment failure may work, as obvious and boring as it sounds. I mean, when you're going at over .5c, there's going to be tons of space dust and space debris in your way. A collision with space dust while going at half the speed of light... not good. So if a spaceship only has 1-2 transmitters, those flimsy things are going to be gone pretty fast unless you have some kind of shields or super-armor.
Alternatively, the crew really doesn't want to talk to Earth in the first place. The captain has always been a rebel against his repressive government, and as soon as they get far away from Earth, he says, "OK, screw them, we're starting our own society here, throw the radios through the airlock". Personally I like jr2's idea the best.