Thats insane. And some have the nerve to rag on my place because it's old. My closet ceiling is 2" wide tongue in groove oak & the original (1916) eye hooks holding up the rod are still there! In all 3 closets!

That is just poor workmanship! No one cares how things function anymore....it's all about the 10/20 (looks like a 10 from 20 feet away). Pay me my money & see ya later.....

Can you take a photo of the closet and the rack that keeps falling down? Maybe we can help you with an alternative. Maybe thick boards at each end going across & put in those rod hooks like in this pic. This might work, depending on how long the rod needs to be.

I have a closet system that is in all my closets and I have a lot of closets. You don't have to have them screwed into studs and it is super strong. It screws into the dry wall with anchor screws. I don't know if you can tell from the pictures what I'm saying.

Are you describing the side wall studs as being in the wrong position for putting up the clothes rod? Otherwise, I'm not understanding your explanation.

I handle this type of situation by putting in wooden boards at the correct height along the sides and back of the closet. If your boards run the entire distance, you can attach them securely at the studs, then attach your hardware to the boards at the location you want. Usually I use 1x4 boards but the exact material depends on what I see laying around at the time. Those boards then serve double duty as the cleats for the closet shelf

This is also the way I put up organizers into the concrete walls of my basement or garage. Take one long board and attach it firmly then you can easily mount whatever items you wish with ordinary screws and avoid the hassle factor of using wall anchors.

Some wall anchors are better than others, but nothing beats directly fastening into the framing.