On an internally regulated alternator (two side by side blades for field leads on side of alternator case), removing either positive or negative battery cable under load can kill the diode. If the diode fries, the alternator will not charge the battery. The diode is replaceable by an alternator repair facility.

If you have an internally regulated alternator, including one wire design, on your '68, be sure that the factory voltage regulator connection is properly bypassed.

Photos of your alternator's connections would help to see what you are working with.