So you saved an outfit, but when you look in that outfit's folder, it's empty. This can happen now and then, and it's caused either by something you're wearing, or something you aren't wearing. That does tend to cover any and all possibilities, but it will be made clear in the solution below.
If you use RLVa there is a chance that it has restrictions that are interfering with the wearing or removing of items that can cause this empty outfit problem, so it is recommended that, temporarily, RLVa be disabled.
In case the problem is caused by something you're wearing, it is recommended that you detach all objects and wear “default” body parts. The easiest and quickest way to accomplish this is to go to the Avatar menu > Avatar Health submenu and click Reset Default (male or female).
This may take a moment or two, depending on the availability of the asset server, your connection quality to the server, and your viewer performance. If it takes a long time, or appears to never happen, try relogging. If you had to relog for step 2 above, try going to a different region, such as Hippo Hollow.
If your avatar still doesn't change, there may be other issues, and the Bake Fail page may help resolve them.
There are two folders, at a minimum, that are involved in your avatar's appearance. The first is the Current Outfit folder. This folder contains links to all the items that you are wearing. If it contains a broken link, or a link not worn, this can cause an outfit save to fail. So, open that folder and delete any broken links, or links that are not shown as worn.
The second folder, in this case, is the outfit's folder itself. Being empty, it is recommended that you delete that folder now.
A third folder may be involved if you are having a particular kind of bake failure: the Lost & Found folder. Normally, Lost & Found contains only objects, linksets and coalesced object sets. If you find any wearables in that folder, delete them. If they are worn, take them off first, then delete. If you cannot detach these wearables, relog, or try going to a different region, such as Hippo Hollow.
At this point, you should be ready to create and save an outfit. For an extra measure of sanity, it is recommended that you relog now. But you don't have to; you can attempt step 6 without relogging. However, if it fails a relog may help.
To ensure that you only wear the items you want in your outfit, manually select and wear each item. Don't try wearing an outfit that you want to modify, as it may contain something causing the problem. Instead, wear one item at a time from that outfit; anything that may cause a problem may then self-identify.
Once you are wearing all you want for that outfit, try to save it again, then check the outfit's folder for content.
If you have identified an item that causes a problem, that item may be corrupt in the SL database. You can try wearing an different copy of that item, if you have a backup of it, or notify the creator of the problem.