Sometimes trees just need a little extra support. Especially trees that were forced by the nursery to grow real tall but don't have a thick enough stem to support it.
I'd take a thin bamboo stick and some nursery tape and add a spine to the central leader so that it's held straight. Remove it at the end of the season. Do not forget to remove it. And don't forget to remove the other stakes you put in once it gets its sea legs and able to tolerate the wind.

I do like what looks like the Reddy-Stake, developed by a fellow alum.

Chinese pistache are notorious for doing this. I've seen it many times. I don't see anything about 'limp' in the botanical sense, but I do see typical reaction in this tree.

Chinese pistache, especially, shouldn't be purchased at a consumer outlet in tall, large, big, huge, giant, big, tall, big consumer choice sizes. Because they need to be staked and trained for an extra period of time until they overcome their floppiness.

I don't know what a bamboo stake halfway up would do, except not allow the plant to get wind-firm. Unfortunately, with a lollipop this size, solutions are few and difficult and involve longer stakes and at least two attachments much higher up the bole for several seasons.

Dan

Thanks for the feedback. Here's a thought that has been lurking in the back of my head:

The leaves on the sagging branches seem to be acting sort of like a parachute or sail--such that they now catch even the weaker gusts of wind. Conseuqently, the sagging branches seem to be getting tossed and turned more and more easily these days.

At this point, do you think I can minimize further damage by trimming some of the leaves from the sagging branches?

...or, is that just a ridiculous idea, and are my branches NOT weakened?

(Feel free to be brutally blunt with your feedback--I have pretty much zero experience with tree care.)

Thanks again.

P.S. One more question: If I do nothing, will my sagging branches eventually become erect/upright on their own again, or are they going to remain arcing downwards from now on?

No that's silly. Don't trim the leaves. They will just grow back anyway. Straighten the main stem with a bamboo stick. I don't know why dan thinks that will be ineffective but it's common to train a tree to have a central leader with a bamboo stick or stake of some kind. It will become windfirm because you're not going to leave it on there forever. When the trunk diameter catches up to the height of the tree it will be more windfirm..

My apologies--I only noticed the additional replies today. In any event, I thought I'd post new pics of the tree. The pics were taken 1.5 months after I thought my sagging branches were doomed: http://tinyurl.com/2ay9ja5

BTW, notice that my stubborn in-laws implemented a rather simple solution for the sagging branchces: They trimmed some leaves.

You don't want that top rope touching the trunk like that. You'll want to purchase a proper tie to avoid inevitable damage.

Dan