I have the same problem. I have just created a Sony support request and will let you know the outcome!
I'm very disappointed that I spend a lot of money on this TV and the PVR feature does not appear to work with USB drives. Also note that the PS3 seems to also have the same issue.
I tried all the things that were recommended on other forums. For example ensuring there is only one partition and formatting to FAT32. The USB hard drive also has its own power supply and so power cannot be the issue.
Does the KDL 32EX310 support all types of USB pendrives? Today I visited a tech store and tried to play some clips via USB on a 32EX310. There were both .mkv and .avi extensions with common codecs, but the TV did not recognised any of the videos.
Is there any opportunity to play these general types (xvid, h264, etc.) on a Bravia?