I agree, a battery dropping to less than 10.5V under load has lost a cell, or has a high-impedance cell.

Or a slipping alternator belt... or a bad diode in the alternator... or a faulty voltage regulator... or worn/sticking brushes in the alternator... or low fluid [acid] in the battery... or dirty/corroded connections on the battery... or a poorly crimped battery cable... or a bad connection on the ground strap... or excessive sulfation on the battery plates... or... well, you get the idea.

Lots of things it could be, almost all of them easy to find, cheap to fix.

tanstaafl.