There is often too much accent on perceived fuel savings with APU operation. Suggest the APU manufacturer be asked for advice if starts unreliable on the ground. Don't always take the word of engineers in operational matters. Opinions are a dime a dozen. Facts are more rare.
Until your maintenance organisation can fix the progblem for good suggest you start the APU at (say) 10,000 ft. With no load on the APU fuel consumption is minimal.
Keep in mind that in- flight start of the APU is recommended if flying in moderate to heavy rain, hail or sleet. This is to hedge all bets if double flameout occurs. This applies at any stage of flight.