Panzer909;
Well, My S was suffering from the very same thing. The car would be fine after a cold started. However once it got warm the needle was below mid-mark on gauge, it would sputter and back fire from idle trough to +6000 rpm. Checked the usual vacumm, plug gap, etc. and also noticed my fuel pressure would change (have a gauge and adjustable FP) and suspected fuel pump for some time now.
I opted to change the eventually replace the DME temperature sensor (next) and upgrade to a HV Bosch 040 fuel pump after much fustration. Flushed the fuel tank, checked the in-tank filter for dirt or clogging (It was clear, like new)

WOW! What a drastic change in personality. Dropped the fuel pressure from 3.5bar to 3 bar (44psi) The exhaust tone got deeper, Idle was steady and rock solid. Still want to replace my iridium plugs (2yrs old) and ignition wires....
DME Temp sensor install pending...
Will post install & updated pics soon.....

Thank you Dave at Lindsey Racing for the Excellent Tech support and products...
PM Me if needed.
Blessings...........
__________________
Guru944
2006 955 Cayenne S Titanium Series - Marine Blue, 1987 Porsche 944S Club Sport.
1987 Buick Turbo-T Lightweight "Great White", +500HP, TA49 Turbo.
http://www.blackbirdmotorsports.com,
944/951/968, 911 and 955/957 Performance Solutions.
Thank you Lord, for your Loving Kindness, Tender Mercy, and Grace. Only You are Faithful.