Perhaps my application experiences may help you decide whether or not to reapply w/your same AMCAS personal statement, Homer...
In early July 1999 I submitted my AMCAS app. I had worked hard to make the personal essay one of the best I'd ever written, and I was really pleased with the end result. (I also have a master's degree in creative writing and literature, which helps!) Northwestern, which screens applicants, sent me a secondary w/o having received my MCAT scores.
Took the August MCAT but knew I hadn't done well and withheld my scores. I w/drew from all schools and concentrated on the April 2000 MCAT. When April arrived, I still didn't feel prepared and decided to sit for the August 2000 exam.
In early July 2000, I submitted my AMCAS primary app w/a revised version of my 1999 essay b/c I felt it still reflected what I wanted the adcoms to know about me. Again, Northwestern sent me a secondary before receiving my August MCAT scores. (Maybe this is routine for them; I don't know.)
Sat for the August 2000 MCAT and felt it went okay. Completed and submitted 25 secondaries. (FYI, I was considered a reapplicant even though I w/drew my 1999 primary app w/o having completed any secondaries.) Of the schools I applied to that initially screen applicants, I received secondaries from Stanford, Drew/UCLA, Loyola, and VCU/MCV.
Eventually, I interviewed at only one school and was turned down by almost every other. I say "almost" because I received an acceptance from that one school and immediately w/drew my application from three schools I hadn't heard from.
Considering all the mistakes I made during the med school application process, I feel extremely fortunate to have received an acceptance. As other SDN members have posted, I wouldn't advise submitting the same personal statement. But if you truly feel that your original essay cannot be improved upon (save for a bit of revising and the adding of some new info), then try your chances. I feel that what most hurt my chances was applying w/August MCAT scores. Whether you write a new essay or resubmit the old, be sure to submit your primary, seondaries, and recs ASAP.
Sorry for this lengthy and detailed response; however, I wanted to provide as accurate an account of my re-application experience as possible. Best of luck to you, Homer.