I had the same problem and it turned out to be a huge vacuum leak.
the Vacuum reservoir failed on my 2003. I also had the check valve that inserts in the manifold to source the vacuum fall out.
So I had very little vacuum to run the SAI system and the other items actuated by this vacuum system.
Get a vacuum gauge. HARBOR FREIGHT $20
https://www.harborfreight.com/fuel-pump-and-vacuum-tester-62637.html . Insert it into the system with a "T" connector and see if you are getting 15 to 20 " Hg reading. I was getting close to nothing in vacuum.
Next test the reservoir. Hook a hand vacuum pump with gauge directly to the reservoir.
https://www.harborfreight.com/brake-bleeder-and-vacuum-pump-kit-69328.html with a plastic line.
See if it will hold vacuum. If not replace the reservoir......they cost about $20.00. The reservoir is made in 2 pieces and glues together. It is a common failure that it becomes unglued. Mine would hold no vacuum. You do not have to un-mount it to test it. Use long needle nose pliers to remove the rubber fitting and attach a hose from the tester.
Look at all the vacuum lines. The lines are plastic with rubber connection pieces. the rubber ages and cracks. I have replaced as much of the Porsche vacuum lines as I can reach with 4mm high temperature silicon hose.
I used a barbed brass fitting to fit the check valve to the manifold. I attached a piece of silicon tubing to this and fitted it to the check valve
There are several good vacuum posts on this site.