It is not entirely clear how this works, although it is thought that the unconscious shift of attention or focus caused by the intense stimulation of the vestibular system temporarily influences awareness. Most cases of anosognosia appear to simply disappear over time, while other cases can last indefinitely. Normally, long-term cases are treated with cognitive therapy to train the patient to adjust for their inoperable limbs (though it is believed that these patients still are not "aware" of their disability).
Source: Wikipedia > Anosognosia
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