There is a program called [SleepWatcher] (http://www.bernhard-baehr.de/) that monitors sleep, wakeup and idleness of a Mac. To start or restart Bluetooth everytime your Mac comes up from sleep, you have to tell SleepWatcher to execute the script from above automatically. Restarting Bluetooth takes approximately 2s, so it doesn't attract negative attention.
The script makes use of BlueUtil, so you have to install it too. (I'm assuming you have HomeBrew installed)
brew install sleepwatcher
brew install blueutil
To make use of SleepWatcher, you have to put the gist to ~/.wakeup (For more information about sleepwatcher open terminal and insert: man sleepwatcher)
After you put your script to ~/.wakeup do the following:
chmod +x ~/.wakeup
Now you can test the script. Add the following command to your terminal:
/usr/local/sbin/sleepwatcher --verbose -w ~/.wakeup
Now you have to enter sleep mode and wakeup your Mac again. After that, you should see the following console output:
Bluetooth is off, starting ...
Bluetooth Module started
Successfully started Bluetooth
sleepwatcher: wakeup: /Users/<username>/.wakeup: 0
If it works, you can set up launchd to start sleepwatcher at login by using brew services.
brew services start sleepwatcher
For debugging purposes you can enter Console App and search for "bt_restarter". Maybe there are some messages indicating a problem.