A319 First Officer reported the auto-flight system missed two altitude restrictions resulting in the flight crew receiving ATC low altitude alerts. Captain disengaged autopilot and flew approach manually.

Narrative

Rainy with low ceilings in ZZZ all day. ZZZ was landing north so we planned the ILS X. At one point on the ZZZZZ arrival; the airplane began to descend through an altitude constraint but the captain caught it right away and corrected. As we were getting close to the transition to the ILS X (maybe around ZZZZZ?); ATC started vectoring airplanes as they turned the airport around to land south. We set up for the RNAV/RNP to Runway XX. Changed the runway and approach in the FMS. The airspace was busy; we were in IMC; and at least light chop/turbulence. Workload was increasing and it was getting hectic. Once I loaded the new approach; I did a quick review. As we were being vectored for the approach; we received direct ZZZZZ1 from ATC. After crossing ZZZZZ1 at 3;000; the plane started its descent to continue the approach. We then got a low altitude alert from ATC; and I suddenly realized that the fix after ZZZZZ1; ZZZZZ2; had dropped out of the FMS and was not visible on the navigational display. I am certain it was there when I reviewed the approach. Closer to the airfield; right around ZZZZZ3; the A/C again began descending below glide path; even with the fix and constraint visible. ATC began to issue another low altitude alert just as we were getting the airport in sight so the captain disengaged the autopilot and hand-flew the rest of the approach visually. We landed without further incident.