My guess is that you have some chips inside the handle assembly that are preventing the handle from returning to the point where it engages. So, it just spins. Given where that handle is located, it wouldn't surprise me.
I don't have a minilathe in front of me right now, but if the handle is like all the others used on jet lathes, it should be able to be taken apart and cleaned out. The problem you are going to have is that without the ability to get the handle to engage it will be hard to break the center screw loose if you have never had it apart before.
Did you try blowing the handle out with some compressed air? Pull the handle as far out as you can (compressing the spring). You should see a smaller diameter area below the handle if you have it out far enough and be able to shoot air in from below. Push the handle in as far as you can (while rotating and jiggling) and shoot air in from the top. If there is something in there, this may get it out.
If that didn't do it, then to take it apart. Since it isn't engaging, you will have to use jam nuts on the threaded part so you can get a grip while you try to unscrew the top.
So, that's what I would do. Not sure if it will solve your problem, but since you are going to replace the part anyway, you don't have a lot to loose by trying. Jet lathes have 5 year warranties. Lathe accessories have 90 day warranties. I'm surprised the handle wouldn't fall under the 5 year warranty. It's an integral part of the lathe, not something you added.
If you don't see where you would use a screwdriver to disassemble the handle, post a picture of the handle (looking at it from the right side of the lathe (showing the "top" of the assembly).
Ed