How do you install closet rods that will last??

Make sure to screw supports in the wall studs at least on one side. If you can add additional supports that is great. Make sure to use heavy weight sheetrock anchors. You might also consider butterfly anchors which go into the wall and then open up to press against the back of the sheetrock for extra support. Getting screws into the studs is the best support.

You need to screw into the studs. if you can't hit a stud use a toggle bolt anchor. Can't just screw into the wall and expect it to hold under the weight of clothes.

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Use the studs or stronger anchors. In our house, we had wire shelving, too, and it fell out as well. We saw that the anchors it used were barely anchors at all! Once we put them back up with better anchors, the problem was solved!

To get a better idea check out how rods are hung in other people's closets. Maybe an internet search might give you some ideas. As the others have stated they must be anchored into a stud in order to hold. Unfortunately not all studs line up with where you want the rod/rack. This is why you will note a block piece of wood nailed into each end of the closet to the wall as the block is nailed into the stud. Then you have a secured anchored block of wood to screw into. I hope this helps.

Better stronger anchors for sure, and maybe something either holding it from the ceiling on either end (against the wall on both ends of the closet use wire or something to take some of the weight off the walls by using the ceiling) also if you're able to use a third anchor on the back wall right in the middle to take the heaviness off the middle from the clothes

The simplest of closet rod holders look like this: http://i.ebayimg.com/images/i/370961717744-0-1/s-l1000.jpg Those with shelves have a bracket design like this: http://tenchicha.com/t/2017/07/socket-organizer-lowes-closet-rod-holder-over-the-door-clothes-rod-shelf-with-hanging-rod-hanging-closets-lowes-closet-shelving-lowes-closet-rods-oval-closet-rod-lowes-closet-rod-tension-c.jpg or like this: https://mobileimages.lowes.com/product/converted/071691/071691458715.jpg

All of them are intended to have the screws go through the drywall into a stud below. So, ideally you would find a stud to screw into. If one side of your closet rod is attached to a stud you may just need to move the fallen side connector over slightly. The stud might have been missed by less than an inch. Standard spacing is 16" on center, so from the first stud there should be one 16" away, then 32", then 48" and so on. You can test a spot by hammering in a nail. If there is a stud below the drywall you will feel resistance to the nail when it hits the stud. No stud and the nail will slide right through.

If you are unable to find a stud you can use molly bolts. These expand on the back side of the drywall preventing the bolt from pulling loose. You already have holes where these would go, and as long as the drywall wasn't damaged when the rod fell, you should be able to use the existing holes as pilots for the molly bolts. Here is a link that explains how to use them: https://www.doityourself.com/stry/how-to-use-molly-bolts