We will be trying to stop and the pedal all of the sudden loses pressure and difficult to stop

Master or slave cylinder blew out. Could be the pressure line also.

There are many things other than brake lines that can cause braking loss. Investigation will reveal the issue. First, check fluid level in the Master Cylinder. If the level is normal, you don't have any broken lines/leaks. If the fluid is full and you have no brake pedal/braking power, chances are the Master Cylinder itself has failed. There are o-rings internal to the M/C that can fail, and when this happens, you will lose pressure to wheel cylinders/calipers and, as a result, lose your brakes.

If the fluid has leaked out, then you need to find out fro where. This is not too difficult normally. Fill the M/C with fluid and have someone press the brake pedal while observing the underside of the vehicle. You should see fluid dripping from somewhere, often near one of the wheels. You can have a leaking caliper/wheel cylinder, brake hose, or metal brake line. Once you determine what part has failed, you can purchase and replace the defective part. Brake calipers, wheel cylinders, and hoses are fairly simple to replace. Brake lines are more difficult, as they require shaping, cutting, and the creation of couplings. After repairs are done, the brake system must be refilled and all air bled from the system or braking will not be satisfactory.

probaly lost fuel pressure, from fuel pump going out, or relay went out. Need more info such as, did engine stop running completly, or did it start back up etc. post back please.

The brake system has air in it or a leak past the seals if it does this while stopped.

Are you losing fluid from the reservoir? A leak.

Can you improve the feel of the pedal by pumping it? Air.

Maybe both if the system has not be flushed or maintained for a while.

THe problem can only really be with the clutch master cylinder. What you describe sounds like the master cylinder is not relieving pressure and this is building up in the salve cylinder, applying pressure to the pressure place and causing the clutch to slip. Can you make the problem go away even temporarily, if you open the bleed screw on the slave cylinder? You say that the free play is correct, but is the master cylinder returning fully to its released position?

If there is a malfunction in the brake servo assist system, and your assistance is reduced, the brake pedal will become hard and you will need much more pressure on the brake pedal to stop the car.

It is possible that there is a vacuum leak in the brake servo assist system and you are only getting 50% or less assistance when you are applying the brakes.

You need to have the vehicle checked out without delay because if you lose brake assistance entirely it will be very difficult to stop the car.

The most likely cause is loss of power assistance to the braking system which means you will need to apply increased brake pressure to compensate for the loss of assistance.

The problem will be with the brake servo assist. It is possible there is a leak in the brake servo assist system, which reduces the vacuum, so you are not getting sufficient mechanical assistance when applying the brakes.

It is unwise to be driving the car with this condition. If you lose all power assistance to the brakes, which could easily occur with this fault, the pedal will become very hard, you will need to apply very high pedal pressure and the vehicle will be very difficult to stop. You need to take the car to a VW dealer for service or to a competent brake specialist in your area to inspect the system and rectify the fault.

VW did a recall on some earlier year models for a leaking brake servo and I understand the problem was a faulty vacuum hose which would fail and leak. I am not aware of any recall for this item on later models like your 2004 vehicle.

All the best.

abs module may be bad if brakes are being applied or the pump is oscillating without pressing the brake pedal.

Brake lights are controlled by one of two means; a switch, normally located under the dashboard which is operated by the brake pedal suspension or a pressure sensitive switch that monitors the hydraulic fluid pressure of the braking system.
The first switch makes contact when the pedal is pushed, the second, when pressure rises in the braking system. .

Either way, the switch has probably failed or is the first type, the pedal is not returning all the way to its stop therefore leaving the mechanical switch in its 'on' mode.

Check for the mechanical switch first under the dash and press the brake pedal just with your hand while you are watching the suspension to see if when you let go of the pedal that it returns to its stop.
Once you let go of it, lift it to see if there is still a distance to the pedal stop.

I have seen this kind of switch get worn or sticky and prevent the pedal suspension from returning completely which will keep the brake lights on.

If you find no mechanical switch under the dash, locating a pressure switch is more difficult since it is likely under the hood and perhaps not easily seen.
You might need a Peugeot mechanic to locate it for you.

First you need to check the brakes lines and the brake pads must be replaced on your car they may be worn out........ Get it checked from the local service center........