Does heavy bleeding during pregnancy, despite the presence of a pulse, and the cessation of bleeding followed by its reoccurrence, necessitate a state of impurity, and consequently, the omission of prayer?

The opinion of the majority of scholars is that a pregnant woman does not menstruate, and any blood she sees is considered Istihadah (non-menstrual bleeding). Therefore, you must purify yourself from this blood and perform ablution for every prayer after its time has begun. Do not abandon prayer.