Keyboard needs to be setup on every boot up
Um, standard "stock" fixes:
- Repair permissions
- Check logs
- Erase (Logitech) software and reinstall
You could also see if it is actually saving the connection details (by finding the pref file) or it is unable to.
Repair permissions: Run Disk Utility; select your (main) disk; click Repair Disk Permissions
Viewing logs: Run Console