I believe the first two pics belong to a mandevilla vine; the third I don't know. Yes- I would definitely rescue it by giving it some tlc- remove dead or dying parts of the vine, dead leaves, water once it's dried out some and place it in a sunny window. You can save it this way for next season.

Thanks for the ID; it does indeed look like a match for Mandevilla. That third photo above looked originally like part of the main plant, but was a neighbor's vine creeping under the fence and through the Mandevilla. Below is a photo with other plants cleared away. The Mandevilla is in the ground, so it's not going anywhere. Other GW posts lead me to believe it can tolerate a hard pruning, so I've trimmed off quite a bit of the ailing leaves. I'll look forward to spring so I can see what sort of blooms it might have.

Wow- you did a great job!

Thanks, Surya; that's encouraging. The first person here to see it after pruning said it looked more lush before I chopped it. (Well, hmph.)

I saved three healthy-looking pieces to try to root. I hope in a few months I'll have some to trade.

The vine is Stephanotis floribunda.

Rgds

The neighbors' creeper looks like something in the Commelina family, if you're still curious. I don't know which Commelinas (by genus) would be in CA, or maybe a Tradescantia or Callisia.

Good luck with the 'real plant!'

Thanks, Dryadella. Stephanotis floribunda looks very close, too. I read that Stephanotis will get pale chlorotic leaves in insufficient sun; are the white leaves in the top photo what chlorotic looks like?

Chlorosis is more uniform on a whole leaf.

Your affected leaves look more like they had a surface pathogen of some type, or minor insect damage on them a while back, or were possible accidentally hit with something caustic, like a cleaning product, weed killer, or even really hot water from turning on a hose sitting in the sun.