Try this...
Turn your Axe off. Plug the cables in. I don't know if you have anything else in the midi loop, but there shouldn't be. If thee is remove it and connect the Axe directly.
Have you absolutely confirmed that both cables are working properly and fully? Do you have other cables you can try?
Run Axe Edit
Click Source and select Axe-Fx
Click Recall and select Refresh from Hardware. It should ask you if you want to back up the banks while you're at it. Go ahead and do it. It'll take a while, but it'll be a good test run.
Now, something to note. When I uploaded my user cabs, I had a bitch of a time too. That preset manager in Axe Edit is a bit funky about that. Dunno if it's a bug or what.
If I want to load something into the Axe I set the source as a preset folder, select the patch I want to edit or upload to the Axe. Click the 123 box next to the name, select bank A and click on the preset you want to upload so it's showing in the editor.
Click Preset Mgr. You should see the patches from the folder on the left. Drag the preset down to whatever number patch you want to write it to. Right click on it and click save to source, but first make sure your Axe is selected as the source in the right side.
As for the cab thing, dunno what the problem is there but as long as you can get them uploaded it's cool.
Honestly, it sounds like a midi timing issue that's causing your problem. Either that or a bad cable. Have you updated your midi drivers to the latest version and tried reinstalling the controller?
Other than that, I don't know what else I can tell you. It's not working on two different computers. You could try contacting Fractal Support and see if they have any suggestion. There's a very slight chance it could be the midi ports on your axe that have a problem, but I find that highly unlikely. Still, the slimest of chances doesn't mean it's not possible.
Good luck with it man. Let me know how it goes.