RCexcl ignition modules can run without problem on voltages down to 3,2V. I have not tested any lower than that.

Ive got a couple of planes with RCexcl modules running with single cell LiPo and have had no problems.

Current drain goes up with higher voltage.
If the input voltage is 6V, the current drain is about 400-450mA average.
If its 3.7V, the peak current drain goes down to 280-320mA on average.

Thats why I use 1750mAh capacity LiPo with a regulator set at 5V output rather than 6V outout or 6V NiMH pack.
I always go with LiPos as I feel LiPos are easier to charge at the field and wont drain themselves.

Higher current drain may indicate high resistivity with on/off switch and/or power connectors.