2007 Prius 12v Battery failures after 2 replacements

Check the connections, including where the negative strap bolts to the body, as it may be rusted or corroded.

How many hours per week are you currently driving?

 

The negative band looks like it has a crack in it whether that's causing you any problems I wouldn't know but connection between your meter and ground and that terminal and moving it around if it can move around while it's on the terminal and the supposedly affixed to the terminal those are definitely not good signs I can't tell from here.

 

Just looking at the point where it attaches to the body is NOT good enough.
Needs to be loosened, cleaned with a wire brush or sand paper and re-tightened.

The crack mentioned is where the cable connects to the negative battery terminal.
It may be damaged........and/or not down far enough on the post.

 

The installation job is poorly done and is likely your problem. Neither of the clamps are fully seated on the battery terminals.
You need to loosen the bolts on the clamps and spread the ends out. Then slide the clamp fully down the terminal until it basically sits on the battery case. Then tighten the clamp. Verify the fastener on the "ground to body" connection is tight.

 

^ that.

Take the clamps off, spread them open a little with a screwdriver, and put them back on the battery.

Then use the back end of the screwdriver to tap them down until they are around the fattest part of the post. (the posts are shallow cones, not straight sided cylinders)

THEN tighten the clamp bolts.

This is 100% bad connection on a good battery.

 

While that may be likely.......you don't KNOW that without being there.
It is possible that the battery has an intermittent connection INSIDE the battery.

 

It would be better if you actually came back to confirm that that was the problem. It is preferable than just leaving it for readers to assume that this what fixed the problem.

 

and that's the way we like it!