At that mileage, the fuel filter is probably ready to be replaced. Have you done that? A clogged filter may cause those symptoms. I replaced the filter on my 19k mile '01 the other day and I couldn't believe the amount of dark gray crap that spewed out of the thing.
I'm not sure if Boxsters are susceptible to this, but some of my previous cars had similar symptoms to yours when the plug wires/coil packs were dried out and cracked, which lead to arcing (mainly causes hesitation, but occasionally killed the car for a bit). It's more noticeable in humid weather, and I think FL would qualify as humid.
Other than that, I don't know. Good luck.
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