5200mAh battery pack only charges 1900mAh battery ONCE?

I bought an external battery pack recently to charge my phone on the go. My phone's battery has a 1900mAh capacity and the pack has a capacity of 5200mAh, a little over twice the size of my phones battery. However, the battery pack only has enough juice to charge my phone fully once, and then about a quarter full. The pack is advertised to only have enough to charge an iPhone 4's battery twice, which is a 1450mAh battery, so the company didn't falsely advertise. But I want to know why if it's capacity is twice the amount of my phone, it can only charge it fully, once.

The pack charges 1amp at 5V. I was thinking maybe some of the power is lost through heat during the transfer? Cause after all no cable or battery is 100% efficient at power transfer/storage, but that seems an awful lot to lose while it's charging. Anybody know what the problem most likely is?

Might be the false advertisement, company's do this all the time, just so they get more purchases and more more unsatisfied customers.

My guess is that the pack could charge your phone twice… If the phone is completely powered off. My guess is that you're killing a lot of the pack's battery keeping the phone powered on while charging.

Who made it?

Is it a decent brand like Uniross or Duracell or something. If not it could be you've been sold some cheap Chinese/Taiwan junk that doesn't really have the capacity as advertised.

Yes it is false advertising but if it's a cheap Chinese company that's made it then your unlikely to get anywhere complaining about it