But the update from 3.1.2 to 3.1.3 was very very minimal and hardly changed anything at all on the phone worthwhile.
Changes from 3.1.2 to 3.1.3
Improves accuracy of reported battery level on iPhone 3GS
Resolves issue where third-party apps would not launch in some instances
Fixes bug that may cause an app to crash when using the Japanese Kana keyboard
Fixes security bugs in CoreAudio, ImageIO, Recovery Mode and WebKit[41]
Renders iPhone 3G/3GS Unlock (blacksn0w) ineffective by upgrading baseband.
Only thing that has changed is the Baseband, the baseband is what controls all of the wireless and bluetooth functions and is a child resource to the main CPU/OS of the phone and has its own firmware. I believe though that the actual connection, i.e. Bluetooth is controlled by the iPhone CPU not the baseband, the baseband just holds the functions, so If my knowledge is correct, even a baseband update will not change the Bluetooth connection.
Try going into settings and doing a full reset of the network connections. If that doesnt help, you could try making an image of your iphone in iTunes, confirm that the phone is backed up, put the iPhone into DFU mode and do a firmware 3.1.3 restore then restore your backed up image from itunes back onto the phone.