After upgrading to OSX Mavericks my BT peripherals temporarily stop working

I have a MacBook Pro 2009 with 4GB Ram, my only BT peripherals are a Logitech BT keyboard and Apple Magic Mouse. After upgrading to OSX Mavericks the day of it's release the overall performance of my MacBook was increased and I was/am very happy with it. My major gripe/annoyance is that upon opening a new application BT connectivity is totally lost and I have to revert back to my MacBook's keyboard and touchpad for a few seconds before BT comes back, and when it comes back it works flawlessly until I open another app or switch between certain apps. This issue is new since the OSX Mavericks upgrade, and my hardware setup has remained unchaged from day 1. It sounds like a software issue, and I was wondering if anyone else has had the same problem or has discovered a solution. I have cycled power on the machine, and have left it completely off for 24 hrs before booting it back up with the same issue. This isn't major, just annoying. The only other thing I have is with Mail and my GMail account seeming not to sync up correctly. Messeges archived on my iPhone 4S still show as unread on my Mail app even hours after the archive and both devices on the same wireless network, This never happened before the upgrade to OSX Mavericks... Everything used to sync up perfectly... Anyone have any ideas as to what may be going on??? Thanks!!