Do your Porsche air pump burn the 7.5 amp fuses?
 

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I have a 997S, not a Cayman, but I have been told that if you use the 12 volt socket that is in the foot-well area of the 911 instead of the cigarette lighter socket, you will blow the fuse. I don't know if your Cayman has multiple 12 volt outlets, but if you do and you are not using the one for the cigarette lighter, that might be your problem.

Yup, you have to use the cigarette lighter socket, I believe it is a 15 or 20amp fuse.