The radar transmitter is pumping out pulses of energy of up to 1,000 watts. The receiver is designed to respond to returning echo signals measured in micro watts, a millionth of a watt. Even if the transmit/receive protection circuits work in around a microsecond, you will see nothing within a 300 metre range. If they take three microseconds to switch over, you are blind to everything within a kilometre. We are talking millionths of a second here to switch from 1000 watts out to a few millionths of a watt coming back! The technology is well proven, but transmit/receive delays increase as equipment ages, so close in blind spots get bigger. A crew may actually perceive the radar equipment as working better as it ages because of an apparent reduction in close in sea clutter.
As stated earlier, very strong local reflections can overwhelm the receiver protection circuits and render the radar blind even at longer ranges. It is possible to tune the radar to reduce transmitter power, reduce or tune out sea clutter, reduce receiver sensitivity, and digitally enhance the display picture, but this takes time and a certain degree of skill to optimise the settings.
Judging from the cockpit transcripts, I am pretty certain that the radar did not display Black Rock in any recognisable form due to the weather conditions at the time, incorrect mode or adjustment of the radar receiver, slow changeover of the transmit/receive protection devices, or possibly overload of the receiver circuits due to very high return signal levels. None of these scenarios would necessarily be apparent or present any real problems to the crew over open water looking for a vessel, particularly at longer range settings.
If Black Rock wasn't showing on the radar display, then the scepticism voiced by the pilot and delay in changing course, in response to the warning from the FLIR operator, makes perfect sense.