The Dyson hose, when stored, hides up under a plastic sheath. To remove it, you have to pull on the hose, which puts added stress on the hose and can result in tears as the hose ages.
I made a slight improvement as well. Although it is a trade off, I also shortened the hose by a few inches so you can pull it out by grabbing the plastic end, instead of pulling the hose.
Step 1: Tools
Step 2: Take the end of the hose assembly apart
This step is the most challenging, and based on others' experiences, the tabs are prone to breaking before coming off. Others have overcome this using different techniques. I've included some tips from the comments, but read through them below to get additional thoughts.
We need to disassemble the hose end first, to cut out the bad part of the hose.
Before you gather your tools, put some water on to boil, to help make this step easier.
First, submerge the hose end in hot water, up to and including the tabs, to soften the plastic and make everything a bit more flexible and workable. Take a quick break, and let the hose soak for about 5-10 minutes.
Now, start by releasing the two black tabs on each side to release the hose. Hold the hose end with the lock button on top and squeeze the sides to relieve pressure on the two black tabs. Using the screw driver, push hard in on the first black tab, then rotate the screwdriver handle towards the open end of the hose, prying the tab out of the hole, until it clicks. Turn the hose end over and repeat for the other side. When the 2nd tab clicks out, the hose will easily release from the hose end.
Be very careful with the gray plastic business end. There are two small springs that are used for putting tension on the yellow lock button. With the hose separated, these springs are lose and can easily come out if you're not careful. They are easy to put back in place if they do come out, but they're small and could easily be lost if you don't keep a close eye on them.
Step 3: Remove the black plastic end of the hose
Step 4: (Optional) Shorten hose slightly
I selected about 1.5" of hose to remove, based on a quick and rough measurement when my vacuum was fully assembled.
Using the wire cutters and the utility knife, clip the hose wire at your selected spot and then finish by cutting through the plastic hose until you have completely removed the extra section of hose.
Step 5: Cleanup hose end
First thing is snipping up the end to make it fit the black plastic piece again. Make a clean cut on the end of the wire, then cut a V into the plastic hose to remove some excess so the wire fits snugly together.
When all cuts are made, wipe down the inside of the hose to remove all the years of dust accumulation. This will help the glue stick to the hose.
Step 6: Cleanup black plastic end
This is the tedious part of cleaning all the glue and glued on rubber hose bits from the black plastic end of the hose. This is also an important step to make sure the clean hose end fits back inside the gray business end of the hose. It's important to make sure the glue has nice surface to stick to.
Use the utility knife to CAREFULLY scrape away anything that's not black plastic. Wear gloves if you have to. Maybe use a vice.
I'll let you determine when it's clean enough since the last two pictures are too blurry to really see.
Step 7: Reconstruct the hose
First test the fitting of the black plastic piece and the hose. Make sure they fit together well, and if necessary, clean up any extra glue, or shave off some extra plastic hose. You want this to be snug and close fitting, and also secure so you have as much strength as possible when everything is put back together.
With everything looking good, place a good amount of super glue around the edges of the black plastic piece where it will make contact with the hose. If you use too much, like I did, you'll end up with some on your hands. If you use too little, you won't have a strong hold. I prefer to err on the side of too much, but be careful to keep the glue off your fingers.
Now wait for the glue to dry. Follow the instructions on the glue that you have chosen and wait as long as you can to make sure everything is secure. I ended up waiting overnight because I had the time, but you don't want to test your connection before everything is dry, or you'll have wasted all your work.
Step 8: Continue reconstruction
If everything looks good, proceed to put the gray plastic piece back on the hose end.
Line up the tabs on the black plastic piece with the holes in the gray plastic piece. With everything lined up, push the two pieces together until you hear both sides click into place. I chose to put the gray piece on the floor and push down hard on the hose.
With everything in place, you should have a good-as-new hose.
If you chose to shorten the hose to make it easier to pull out, when you stow the hose and clip the hose/tube assembly back into the main vacuum, you may encounter a slight bit of resistance the last few inches before everything clicks into place. I believe the vacuum is designed to push the hose end up into the plastic sheath, but with just a bit of an angle adjustment, you should be able to easily put everything back into place without the hose end going back into its hiding place.