Theoretically, most projects fail during the planning phase, because it's the bad planning that usually leads to project failure. Whether it's bad requirements captured in the project plan, or bad risk management plan, or bad communications plan, or bad change management plan. In my opinion, it is all in the planning.
Technically, the project fails during the executing phase, because the project, and in 99% of the times, even if it's badly planned, goes to the executing phase. It is in this phase that everyone starts discovering, slowly but surely, that the planning was bad (unrealistic project schedule, unrealistic budget, etc...).