I've had this problem with 2 of my panthers. Initially, I thought it was the alternator; turned out to be bad starters.
Currently own 2 panthers;
2002 Crown Vic LX Sport(black- of course)
1993 Grand Marquis LS (silver) with 210k; looks good, runs strong. Highway package....
GONE BUT NOT FORGOTTEN.....
1992 Town Car with 170k; (sold)
1993 Grand Marquis GS(silver) with 323k; still running strong.(sold)
1989 GM LS with leather
1997 GM HPP -damn i miss that car...:(