I remember reading older threads that said USB charging could actually drain a battery rather than charge it. I don't recall whether it was in a Sony or some other device context or whether it was addressed to newer or older devices, but you might search MobileRead for "USB battery drain" and see if you get any hits.
I personally never liked the USB charging. I always found it slow at best. With my Sony 505 I bought an
iGo system and used a PSP plug to wall charge. With the Sony 950, the charger that came with the device is wall pluggable and I used it until I bought the correct adapter for the iGo system. I'm not familiar with the 650's charging system (that is, the one that came with the device), but I assume that Sony is supplying the same charging system across devices. If they are, try wall charging. If not, consider buying the iGo system. I use it to charge my cell phones, both of my Sony Readers, and my cellphone headset, both at home and when traveling.