I was waiting to see if anyone would reply, because at Pico we're not in the business of randomly endorsing a product, but as they haven't, I can share my experience with you as a consumer, and in no way connected with Pico Technology. The orignal 6404 PicoScopes consume approx 2A with all functionality being used. So, worst case, you need a good battery range up to 'several x 4Ah' to cover your requirement of several hours. I have used this Tracer Range: http://www.tracerpower.com/tracer-lithi ... packs.html
for various powering applications, and found them to be excellent on retaining charge when not in use, fast to recharge, truly portable, and ticking pretty much all my other boxes. However, battery power is a fast growing development area, the Tracer range were relatively new and original a few years ago, and there may well be more cost-effective/applicable solutions out there.