A problem I see every day at work is techs replacing parts hoping this will take care of the problem. Many things can affect the OBD II system and after bring up the fault codes the tech need to run a few test to confirm the problem not just replace parts.

DTC P1123 - oxygen sensing adaptation range 1 (cylinders 1 - 3) lean limit
The oxygen sensor generates a voltage signal at approximately 572 degrees Fahrenheit (300 degrees Celsius) that determines the fuel/air mixture. The signal is used for the regulation of the fuel injection. The oxygen sensor is heated to bring it quickly to operating temperature to start oxygen sensing earlier

DTC # Fault conditions Possible cause
P1123 Fuel / air mixture is so rich that the control is up to the lean limit Fuel pressure too high
Fuel injector leaking

Diagnosis conditions
Oxygen sensing is active
Time elapsed after engine start-up is 250 to 350 seconds.
Engine temperature above 144 degrees Fahrenheit (62 degrees Celsius).
Intake air temperature below 194 degrees Fahrenheit (90 degrees Celsius)
Air mass flow above 29 kg/h
Engine speed above 880 rpm.

Test 1 - Checking fuel pressure.
Remove fuel pressure test cap from fuel injection rail.
Connect fuel pressure gauge using Baum tool 378 and Porsche adapter 9559 to test port.
Actuating fuel pump:
With scan tool
The fuel pump can be actuated with the scan tool or by bridging the fuel-pump relay.
Bridging relay
Remove the fuel-pump relay from the central electrical board and bridge terminals 30 and 87 (identified as 3 and 5 on the relay panel) with a fused shop-made test harness. The fuel pump must now operate and deliver fuel.
Nominal test values:
With engine off 55 + - 3 psi (3.8 + - 0.2 bar)
With engine running 48 + - 3 psi (3.3 + - 0.2 bar)
The test port seal is not replaceable, the cap must be replaced after removal.

Test 2 - Checking fuel pressure regulator, vacuum connection and fuel return line.
Remove vacuum line from fuel pressure regulator.
Connect vacuum hose to a vacuum gauge.
Start the engine.
Specification - 0.4 - 0.6 bar
If the value is not reached, check vacuum system for leaks and check vacuum line to fuel pressure regulator for restrictions.
Check fuel pressure housing for damage.

dtc P1124 - Oxygen sensing adaptation range 1 (cylinders 1 - 3) enrichment limit
The oxygen sensor generates a voltage signal at approximately 572 degrees Fahrenheit (300 degrees Celsius) that determines the fuel/air mixture. The signal is used for the regulation of the fuel injection. The oxygen sensor is heated to bring it quickly to operating temperature to start oxygen sensing earlier

DTC # Fault conditions Possible cause

P1124
Fuel / air mixture so lean that the control is at the enrichment limit Intake system leaking
Fuel pressure to low
Fuel injectors contaminated
Volume supply of fuel pump to low

If DTC P1124 or P1126 is in the memory, this means that the fuel/air mixture is too lean.
Diagnosis conditions
Oxygen sensing is active.
Time elapsed after engine start-up 250 to 350 seconds.
Engine temperature above 144 degrees Fahrenheit (62 degrees Celsius).
Intake air temperature below 194 degrees Fahrenheit (90 degrees Celsius)
Air mass flow below (29 kg/h)
Engine speed below 880 rpm

Test 1 - Checking fuel pressure.
Remove fuel pressure test cap from fuel injection rail.
Connect fuel pressure gauge using Porsche tool P 378a and adapter 9559 to test port.
Actuating fuel pump:
With scan tool
The fuel pump can be actuated with the scan tool or by bridging the fuel-pump relay.
Bridging relay
Remove the fuel-pump relay from the central electrical board and bridge terminals 30 and 87 (identified as 3 and 5 on the relay panel) with a fused shop-made test harness. The fuel pump must now operate and deliver fuel.
Nominal test values:
With engine off 55 + - 3 psi (3.8 + - 0.2 bar)
With engine running 48 + - 3 psi (3.3 + - 0.2 bar)
The test port seal is not replaceable, the cap must be replaced after removal.

Test 2 - Checking volume supply of fuel pump.
Precondition:
Fuel filter and electrical supply in order.
Relieve pressure in fuel tank by opening tank cap.
Connect scan tool.
Raise vehicle and position it in a horizontally level position using a lift or suitable jack and safety stands designed for automotive use.
Make sure the vehicle is firmly supported on jack stands designed for the purpose. Place the jack stands beneath a structural chassis point. Do not place jack stands under suspension parts.

Remove rear underside protection panel.
Disconnect fuel return line. (Have a shop towel ready to soak up residual fuel).
Place fuel line in a measuring container. Actuate the fuel pump with using Baum ISCAN scanner or by bridging relay socket and allow fuel to flow for 30 seconds.
Specification - 850 center meters after 30 second of fuel pump operation.
Test 3 - Fuel injectors contaminated.
If checkpoints are negative, the fuel injectors may be contaminated (carbonized).
Clean fuel injectors. (ultrasound cleaning device) or replace.

DTC P1125 - oxygen sensing adaptation range 1 (cylinders 4 - 6) lean limit
The oxygen sensor generates a voltage signal at approximately 572 degrees Fahrenheit (300 degrees Celsius) that determines the fuel/air mixture. The signal is used for the regulation of the fuel injection. The oxygen sensor is heated to bring it quickly to operating temperature to start oxygen sensing earlier

DTC # Fault conditions Possible cause
P1125 Fuel / air mixture is so rich that the control is up to the lean limit Fuel pressure too high
Fuel injector leaking

Diagnosis conditions
Oxygen sensing is active.
Time elapsed after engine start-up 250 to 350 seconds.
Engine temperature above 144 degrees Fahrenheit (62 degrees Celsius).
Intake air temperature below 194 degrees Fahrenheit (90 degrees Celsius)
Air mass flow below (29 kg/h)
Engine speed below 880 rpm

Test 1 - Checking fuel pressure.
Remove fuel pressure test cap from fuel injection rail.
Connect fuel pressure gauge using Porsche tool P 378a and adapter 9559 to test port.
Actuating fuel pump:
With scan tool
The fuel pump can be actuated with the scan tool or by bridging the fuel-pump relay.
Bridging relay
Remove the fuel-pump relay from the central electrical board and bridge terminals 30 and 87 (identified as 3 and 5 on the relay panel) with a fused shop-made test harness. The fuel pump must now operate and deliver fuel.
Nominal test values:
With engine off 55 + - 3 psi (3.8 + - 0.2 bar)
With engine running 48 + - 3 psi (3.3 + - 0.2 bar)
The test port seal is not replaceable, the cap must be replaced after removal.

Hope this helps BW

I have run into the same problem on my 2001 996 c4 with 54,000 miles. I just purchased the car a few months ago and do not know any of the past history. Have you solved your problem yet? If so can you tell me what you had to do, Thanks. I am going to try replacing the fuel filter and clean the MAF sensor. I had the car in the dealer for a trans issue and they also saw the error codes and told me that for about $540 they could trace out the problem. The service manager after I picked up the car told me that he thought it's the MAF sensor. We will see.

Two things come to mind , first it's the wrong Air Mass meter, according to vin # there is a split,the second is what I've run into at work a few times usually the 1123 code.
What is probably happening is there are air injecton ports in the heads and around 60,000 they become clogged with carbon which does not allow the injection pump to pump air into the heads during warm up this sets off the codes. The engine at this point usually needs to be torn down to the heads, all the valve guides need to be replaced, the heads and intake manifold need to be bead blasted to get the carbon out.

I have heard of a alternative but the results vary and you still need to remove the engine, turn engine upside down , remove exhaust system and pour a injection /carbon cleaner into the exhaust chambers and let sit for a few days, this might work may not

The crankcase breathers are really bad on these and to look at them from underneath they look ok but only takes a little split and your dme gets all confused and under/over fuels causing it to cut out and throw codes.