If your battery hits 10.5v, as stated, it's pretty much time for a new battery. Or it needs some serious attention to eek some more life out of it. If it's a lead acid battery it takes maintenance! Fully charge the battery, as much as it will accept. Then let it rest for 24 hrs. Check the voltage then, that is its resting voltage. If it's below 12.2-12.3 you will not be getting much more life. A healthy battery will rest at 12.6 and above.
After it has fully charged and rested: Open the top - with Chem resistant gloves and goggles, check the fluid level. It should be close to the top, maybe 1/2"-3/4" down, either way all of the plates need to be submerged. If the plates are exposed then your battery is already in bad shape. If low, fill with distilled water until the plates are submerged. Then charge, rest, and test again.
If it fails the above then it's new battery time.
I would not personally entertain wasting money on a Chinazon ACR that is labeled, "High Quality"