Pickling is only supported on python's built-in data structures and composites of those. The caffe._caffe.Blob is merely a python interface to the underlying C++ datastructure.
But why would you want to do that anyway? For serialization you could either use the protobuf format (which is kinda 'native' to caffe), or convert the contents of the blob to a multidimensional numpy array, and save this to a npy file:
blobdata = np.array(net.blobs['blobname'].data[:], dtype=float, copy=True)
np.save('blob.npy',blobdata)