I'm trying to figure out the frequency response of my subwoofer. The manual says overall range 30Hz-180Hz but then it also says -3dB limits 40Hz-160Hz.
Which is the most accurate frequency response? How can I avoid the -3dB limits so that I can always achieve the 30-180Hz performance?

The short answer is....you can't avoid the rolloff. Speakers are designed and specified to produce frequency ranges. However, the physical design of all the components will determine the actual output at a particular frequency. The speaker can produce at many frequencies, but design limitations dictate that it will be less effcient at all frequencies. It will produce sound at these frequencies, but simply with less volume levels for the given input. As it approaches the limits, or even certain "in band" frequencies, it can produce less.

Remember that speakers are really electrical motors...very inefficient motors at that. Typically speakers are less than 10% efficient at turning amplifier energy into acoustical energy - with most being about 4% and some about 1%.

So basically what you're saying is that unless I run the sub at max volume, I'm not going to achieve the 30Hz end of the spectrum on a consistent basis?

No, you will achieve 30hz at most volumes, just a limited level of output. To run the volume very loud will produce more at all levels or frequencies, but the proportionate levels will almost always apply.

If my mathematics is correct, to raise output levels by 3db, you need to double the volume levels, meaning a doubling of input signal.