During a side-slip at an excessively steep angle of bank, it may not be possible to control yaw. Why

The straight sideslip is limited by the maximum rudder authority available, there will be a bank angle beyond which full opposite rudder will not stop the aircraft from turning.
The rate of turn and the rate of sink are controlled by the amount of bank and the amount of rudder but it is an uncoordinated descending turn. Dangerously high descent rates are achieved if the bank angle applied exceeds the full rudder authority.

Good question: When an airplane begins a turn, the Lift vector splits into 2 components, Vertical & horizontal.

The more the bank is increased the greater the Horizontal force while its being supplied by the decreasing Vertical Vector. Centrifugal force is the force that opposes a turn. If both the Centrifugal force & the Horizontal force r equal we can say that we r coordinated.

We all know that when the vertical lift is reduced the pilot must compensate with the elevator, therefore, increasing the lift & drag on the wing & slowing the airplane.

NOW, if max rudder were used to oppose the turn while in a bank we can now say that we have increased the Centrifugal force considerable to prevent heading changes.

There r 2 main reasons why the airplane will yaw:
1.The bank becomes steep enough where the rudder cannot compensate for the corresponding bank.
2. For the corresponding bank the rudder has lost its effectiveness due to the lose of airspeed.
In this case Airspeed in not the only factor as CG also plays its part in the leverage between the rudder & the vertical Axis (Yaw Axis). The speed at which u start to see a yaw could be diffrent, because of density alititude, CG location, Weight, Power setting, & bank angle.

For Multi-Engines u can find similar factors.

Good Luck

In an extreme side slip the ailerons become totally ineffective.

There r some very complicated above that r correct. To speak in plain English though: In a high degree of bank angle, a lot of rudder input is needed to maintain directional control (to keep going straight). If ur slip is deep enough, the fuselage may block the relative wind from flowing over the rudder. This means ur rudder do not work no more. It is effectively stalled (just like ur wings would be if u flew too slow).

In order to prevent this from happening, maintain a safe airspeed. A stall at that type of attitude typically happens close to the ground & results in a spin/spiral with little altitude to recover. i.e. Death

Short & sweet answer equals: at high bank angles there may not be enough airflow over ur rudder to keep it effective.

--May be true in some planes.

I've used full rudder deflection when spiraling down in banks much steeper than 70º and have not had any problem controlling yaw.