Have had my surface pro 3 for less than 4 weeks, and over the last week with increasing frequency my pen has been intermittently not working (the tip and buttons, not the 'top' button). I have ordered new batteries, but would be surprised if the batteries only lasted less than a month with light usage. Anyone have an idea as to how long the batteries should last, or is there possibly something wrong with the pen? I've tried unpairing/re-pairing without any success. Thanks!