Worn down brake pads won't cause the symptom you describe. What would happen would just be a lower brake pedal than normal, not a lack of any brake power at all.
A bypassing master cylinder means that the seals inside the master cylinder are worn/broken allowing fluid to bypass the plunger, causing the fluid movement to become weak, therefore losing braking power. Pumping the brake causes the pressure to build back up momentarily. You can bleed the brakes and have what seems like fine fluid travel, but under driving conditions, that isn't enough.
The only other practical cause for no pressure would be brake leak somewhere, such as in a line somewhere.
Do this: turn the car on, pump the pedal until pressure returns and hold the pedal down. If it starts to fall, the master is likely bypassing.
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