Control a switch with headphone output jack
This sort of pop is a common problem with audio connections, particularly guitar leads as they can get swapped live. It's caused by capacitance in the systems being connected holding different dc levels, and results in a step pulse in the power output stage, which isn't good for your speakers and probably is what overloads your battery. 

One means to neutralise is a reed switch in the jack, though I don't know of a mini stereo version. 

The other means are to reduce capacitance in the cables and input stage of the amp. It may also be possible to use a transformer to isolate the input, or possibly a band pass filter to remove both the suddenness of the step change and the dc offset. But a filter may well have to be in the audio range to be effective, and that is the range you want to maintain.

If there was an automatic circuit which did this well then every electric guitarist would buy one, and there doesn't seem to be any out there (normally you have manual mute switches or the fore-mentioned silent jacks), so if you do get it to work there's quite a market.

An answer in another question pointed to this circuit as a possibility.