Is there still a need for reduced voltage starting methods? Around these parts there generally is no need for that until you get over at least 100 HP motors, or if mechanically "soft starting" is desirable - but that is usually done via electronic soft starters that have even greater "ramping control". An autotransformer starting method was primarily for reducing the amount of surge otherwise encountered when starting across the line. Improvement in the supply over the past 40 years may not require this anymore.
Chances are something in the present control scheme is malfunctioning, could be a pushbutton contact, holding contact on a relay/contactor, hung up contact on a transition timer, or intermittent operation of any of those things if it is not consistent in nature.