If you find orders are not completing/processing after payment (either via PayPal IPN or any other gateway) and you are running W3 Total Cache, check the PURGE POLICY settings. Go to: Performance > Page Cache > Purge Policy
To turn off the purge policy for POST COMMENTS PAGES and POST COMMENTS FEED deselect the checkbox. These can make the request timeout or run out of memory, breaking the order status update.