Mobile communications device providing heuristic security authentication features and related methods

A mobile communications device may include a plurality of first input devices capable of passively collecting input data, a second input device(s) capable of collecting response data based upon a challenge, and a processor capable of determining a level of assurance (LOA) that possession of the mobile communications device has not changed based upon a statistical behavioral model and the passively received input data, and comparing the LOA with a security threshold. When the LOA is above the security threshold, the processor may be capable of performing a given mobile device operation without requiring response data from the second input device(s). When the LOA falls below the security threshold, the processor may be capable of generating the challenge, performing the given mobile device operation responsive to valid response data, and adding recent input data to the statistical behavioral model responsive to receipt of the valid response data.