I think this is an unhappy coincidence as I had/have no USB problems with avast 5.1.864. I have an external 500GB drive that I use for back-ups also and I have just fired that up and no problems, see image.
Your report here is the first that I have seen in the forums, certainly in relation to 5.1.864. So I rather doubt trying the 5.1.874 pre-release version will change that, but you can certainly give it a try.