I tried the identical setup (BT GPS virtually next to BT Receiving module on Netbook) in multiple locations, and got the identical problem.
Move the GPS 3 ft away, restarted, and problem went away.
It can be that ASUS, a known chintzy maker of cheap stuff, used a real cheap module.
I will try the test you suggested when I am on the road --- the trouble is indicated by a "solid" blue LED on the GPS that normally blinks when the BT link is fine.