It depends what you mean by expire. The 10,000 miles are useful in two ways:

1) 10,000 mile to use as currency for free flights and other awards. These miles don't expire for several years (or never with continuing account activity).

2) 10,000 miles towards medallion qualification. These miles are only counted in the year you earn them, but it really isn't a matter of having them expire. If you had enough other medallion qualifying miles to make a particular status level when combined with the 10K, then they were useful to you. Otherwise they are not. Of course if the 10K do bump you up to the next elite level then your status will be good for all of 2004.

I don't think calling AmEx is going to change anything.