Over the years BlackBerry devices have needed more power and the latest BlackBerry 7 devices are the hungriest. Back in the day it used to be a matter of drivers not being installed on your PC and getting the "USB charging current is insufficient" error though sometimes those solutions work today. That error has more or less gone away but recently with the popularization of portable chargers we have been seeing more and more of the new "The Charging Source Connected To Your BlackBerry Device Cannot Charge Your Battery."
From what I have seen this message happens on BlackBerry devices (and many other devices) in one of two cases. First is if the PC does not have the BlackBerry drivers installed or mistakenly identifies the BlackBerry as a mass storage device. The other one is when a portable charger or USB wall/car charger does not know how much current to send to the BlackBerry and so it defaults to less.
For now the best solution I have found to this problem is what is called a charging only cable. (it does not work for data) Many portable chargers use this design of including a charging only cable but others like Mophie’s Juice Packs do not and thus do not charge your BlackBerry even though they can. When you don’t use a charging only cable the BlackBerry thinks it is connected to a computer and thus looks for the driver that will allow it to charge at a higher rate.
I am really hoping RIM solves this issue in BlackBerry 10 but until then you can either buy a charging only MicroUSB cable or many times you can repurpose a MiniUSB to MicroUSB converter on an older charging cable to make them data only. The best charging only cable I have found so far is from Naztech for ~$7.50 on Amazon though I have seen them cheaper on eBay. This cable works wonders with my portable battery chargers and my international travel USB charger/adaptor. It fools the BlackBerry and many Android devices into thinking they are plugged into an AC adapter by shorting the data wires and leaving the charging cables. You can do this yourself with some know how and online guides but I would not recommend it unless you have time to spare.
Let me know if you have found any other solutions to the dreaded "The Charging Source Connected To Your BlackBerry Device Cannot Charge Your Battery" error.