SOLUTION! Here is the solution that worked for me.  I've gone from Bluetooth connections lasting only a few minutes to having no dropped connections in the last 24 hours. In a nutshell, you need to download the Wireless 370 Bluetooth driver for the Dell Studio XPS model 1647.  This driver has Widcomm version 6.2.0.9603 (instead of 6.2.0.9600).  You can download R235898 from here (full downloaded file name is DELL_WIRELESS-370-BLUETOOTH-_A02-1_R235898.exe).
How many people are experiencing this problem?  I've seen several other posts of others with the same problem with no resolutions. In a nutshell, in my Studio XPS 16 (1645), my Bluetooth radio is not able to maintain connections to any other Bluetooth device for more than a few seconds to a few minutes.  When a device connection is dropped (or locked up, haven't fully discerned which one is going on), all the active Bluetooth devices are dropped/locked up and I am also unable to find new Bluetooth devices.  This is rendering Bluetooth useless on my brand new laptop.  The Bluetooth 370 radio stays in this state anywhere from minutes to requiring a full system reboot.  My Bluetooth mouse, keyboard, numeric keypad, cellphone, and printer all are non-function with the 370 Bluetooth radio. Here's what I've tested so far: I'm running a clean installation of Windows 7 Ultimate 64-bit.  My 370 has HCI Version 4.20936 and LMP Version 4.16957. As a result of the testing above, I'm strongly suspecting a hardware failure in this particular card (i.e. a manufacturing defect) or a firmware bug.   There is probably more that I can test and I should probably take a closer look at the Windows System logs, but thought I'd share what I had so far.  I believe that I'm seeing the same issue that other folks are seeing and I'm hoping my additional testing above helps shed more light on this issue.
Dell Wireless 370 Bluetooth Mini-card not working properly (connection 
failures/disconnects/lock-ups)