If a remote is programmed to a car, holding the lock and unlock at the same time resynchronizes the key fob. Solder joints on the battery hold downs are really bad for breaking. Yours is most probably broken internally. A few autoparts stores have testers for them. They're usually at a battery stand and will flash a light if they detect a key fob frequency, showing yours is putting out a signal or not.
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'13 Mustang 3.7V6 - MT82
'00 GP SE (L67 Swap, XP, Headers, 3.25")
'98 GTP, '01 Bonne