Prolonged operation of a mixer in air is not impossible, but seems unnecessary, especially for four hours.  The problem with running a mixer in air involves the natural frequency (critical speed) for the mixer shaft.  If the mixer is designed with a natural frequency too close to the operating speed of the mixer, undamped vibrations may occur causing the shaft to vibrate out of control and bend.
 
I know that I don't have enough information about your mixer to accurately estimate the mechanical design, but based on typical values, I can understand the problems.  First, for the shaft length and tall tank shows that the shaft is likely to operate above the first natural frequency of the shaft.  To do this, the shaft must pass through a critical speed on the way to the normal operating speed.  If the shaft is straight, the impellers balanced, the speed increase rapid, the mixer should not have serious problems.  However, while passing through the critical speed, the mixer could experience severe vibrations, especially when operated in air.  Second, the shaft design is at the lower limit of strength.  If the shaft were designed with sufficient strength to operate with an impeller at the liquid level, as with filling or emptying the tank while the mixer is operating, it should be 76.2 mm in diameter or larger.  The smaller shaft may move the critical speed away from the operating speed, but also make it more prone to fatigue failure.
 
I can understand the mixer manufacturer's concern about operating in air.  Any mixer operating in air is more likely to experience natural frequency problems than when operated in liquid.

Properly designed, the mixer could operate in air and also operate with varying liquid level, but the design may have to be increased in strength, with the accompanying cost increase.  Your design is difficult, because the minimum design makes the mixer more economically attractive, while also limiting some of the operating variability.
 
Good mechanical design is essential and should not be overlooked, whether the mixer operates in air or not.  This design may be just fine, however operating in air or with changing liquid level should only be done if absolutely necessary.  Click here to view a document that explains how to do mechanical calculations for mixer shaft design.

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