Welcome to the world of iOS Bluetooth, where it’s hard to say anything at all about how it works (;
In all seriousness though, our suspicion is that when you don’t use the iPhone for a while, it goes into sleep or low-power mode or something like that, and that’s when Bluetooth discovery slows down. There’s little we can do to change this behavior.
If you have any Location Beacons, you could beta-test our own monitoring implementation, Estimote Monitoring:
In there, we’re experimenting with some tricks to make the Bluetooth detection more responsive. I know a major update is coming soon to it, with improvements to background detection, so it might also be worth keeping an eye on our iOS SDK GitHub repo. (star/watch it to be emailed by GitHub with any new release)