As Captain Gyro points out this is completely untrue! It is quite possible to slow the gyro from cruise speed to zero forward speed and have no material change in the rotor RPM. At zero airspeed the gyro will start to descend vertically, completely controllable and with normal rotor RPM. To exit this state all that is required is to pitch the nose down, attain flying speed and fly the plane, assuming you have enough altitude in the bank.
In a tight turn the rotor RPM will actually increase with the increased G loading, NOT bleed off.
Clearly these incredible machines are very misunderstood. Yes they are easy to fly. But like any aircraft they have a few places where they will bite, and bite hard. Every single gyro pilot is trained to avoid these situations. (for example attempting negative G manoeuvres where the rotor RPM will decay, sometimes with catastrophic consequences).
Getting behind the power curve is one area that has bitten new and experienced pilots alike. Put enough hours in and you should be able to "feel" when the gyro changes from horizontal to vertical flight without looking at your instruments. One area where gyros differ from fixed wing aircraft is that they have no stall warnings. Slow down your airspeed and at some point you'll start to descend vertically, with no stall warning buzzer etc. (The exact point will vary depending on the density altitude, load, etc). The training syllabus teaches pilots to recognise this but a pilot distracted by external factors (wowing a crowd or dropping ashes) might miss the subtle change in flight attitude. Many pilots have been bitten by this specifically on the downwind leg in the circuit and the resulting mush into the ground has been blamed on a sudden downdraft. (See Learjet's post on the dragon of the downwind).
Bottom line is that like any aircraft you need to give yourself options in the event of a problem. Speed and altitude are your friends. Yes these machines can be landed with zero forward roll and in a much tigher/smaller area than a fixed wing, but there is no magic involved and no substitute for safe flying. An engine out while low and slow is probably not going to end well for most pilots...