B737-700
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Situational Awareness
Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Aircraft; Human Factors
On arrival into LAX on the HLYWD 1 STAR after getting cleared for the ILS 25L; the Captain (Pilot Flying) set in the FAF altitude into the altitude selection window and confirmed the aircraft was in LNAV and VNAV PATH.  At some point the aircraft dropped out of VNAV and started to go low on the mandatory altitudes at KRAIN; TAROC; DYMMO; FUELR; GAATE; and HUNDA and reached the altitude of 1900' which was set in the window. At that point I noticed that we were low in reference to the ground and commented that we were low; at which point the Captain rechecked the aircraft automation and saw that the VNAV had disengaged somehow; and was not provided altitude protection on the mandatory points aforementioned. We were visual with the airfield still [in sight] at that point.  ATC asked us of our status and noticed we were low and asked if we were visual with the airfield as well; to which we replied we were. We continued in at 1900' MSL and intercepted a visual glide path at 1900' to land uneventfully on Runway 25L.Everything was accomplished in accordance with proper procedure when it comes to being cleared for the approach while descending with the STAR; the LNAV and VNAV was confirmed before setting in the FAF altitude; and somehow the aircraft became disconnected from VNAV without anyone noticing until it was much later. The prevention of a situation from occurring again lies in not only accomplishing the procedures correctly but also continuing to check more frequently that the aircraft is in fact doing what it's supposed to; even after you already knew it was. This is a case of too much of reliance on automation and thinking that just because the aircraft and FMS were doing what they were supposed to at first; doesn't mean they will continue to do so throughout the flight. An increased crosscheck of FMS errors and possible deviations would hopefully catch an error much sooner and prevent a deviation like this from occurring again in the future.
B737-700 First Officer reported the aircraft descended below charted altitude on approach to LAX when it dropped out of VNAV.