Thanks for the replies, guys. I appreciate them.
Well, I reprogrammed the ESC so that it has no low-voltage cut off, whereas before I probably had it set it at 3.4 v per.
Under this setting, I wasn't able to get the buggy to act like it did. So it could be bad batteries after all. Then again, I only ran it in my backyard, but I was trying to go full speed at every chance -- billowing through all that Autumn foliage like a dolphin underneath water.

But the jury is still out.
When the car would start acting up, it would do so even when I was 50% or lower throttle or speed.. it was just start slowing down and down, and then stop for a full 2 or 3 seconds and then -- back to full blast if I wanted it.
Anyway, I think it's the battery. I couldn't find my battery connectors with the balance plug, which is why I was asking you guys to give me suggestion. But I found the balance plug a while ago but I just wanted to drop in again.
What I'm wondering is: If it is the LVC, then why isn't the red led flashing? I have a Hobbywing. According to the manual, it woudl flash red when it goes into LVC mode...