That's strange Torr.
The preheat phase should not drain more than 15 amps. Most batteries would handle that without dropping voltage too much .

Basically you need to check the impedance of your battery. This is even more important than the capacity in this case. The impedance will tell you "punchy" your battery is. The lowest impedance, the less voltage drop during a big current drain.
You can find very large capacity Nimh packs with very high impedance ( up to 400 mOhm ) in that case the voltage will drop so much during a current drain condition, that it will not be sufficient enough to sustain normal system operation.
What you need to have here is a 10 mOhm impedance pack maximum. Most Lipo packs will fulfil this condition.

Note than pack in series will see their impedance added.
Pack in parallel will see their impedance reduced ( 1/i total = 1/i1 + 1/i2 )