> Do missile systems also lose track of their position midway through a flight like our phones?

Civilian grade GPS receivers are intentionally crippled to stop working above some altitude/speed limits.

EDIT: It seems that the COCOM limits apply only after "1,900 km/h at an altitude higher than 18,000 m".

However, looking at the ublox receivers as an example, they have to be explicitly configured to operate at aircraft-level speeds, which smartphones likely aren't.