Jado 599 ceramic valve cartridge stops working (no water). When I pull out the cartridge, the rubber washer that covers the ceramic disk inside the cartridge pops out. When I re-install the cartridge it works for a while but the valve ''chatters'' at anything less than full open. Then it fails again.

go ask a local plumber we do not have that make here

vinegar and old toothbrush to work it in the threads. let sit for a few minutes. repeat.
keep trying gently.
try tightening it a TINY bit before unscrewing.
vise-grips with rag wrapped around.

cartridges are one piece unless
cartridges replace the insert and tap washer

if it was new,it was defective or installed improperly

Sounds like you installed the cartridge incorrectly. The orientation is important to note when removing the old unit. Try pulling it out and reversing the orientation. Check the inlets and match them up.

Check the inside of the faucet for debris blocking the cartridge or the inlets.

On the cartidge there should be a little stopper on the stem that sticks out where the handle goes on ( this prevents the handle from going all the way up ) try repositioning this stopper. good luck

These faucets can leak in three different places:

1. Internally at the valve seat
   You'll see water dripping from the spout. This means the rubber washer is worn or damaged. To replace the washer, remove the decorative cap from the handle. Remove the retaining screw and pull off the handle. Remove the decorative cover, called an escutcheon, if there is one. Unscrew the packing nut counterclockwise. Unscrew the valve stem and remove it. Remove the screw that holds the rubber washer in place. Because these washers come in many shapes and sizes, you'll want to take the old one to the hardware store and buy an exact replacement. Be sure to buy two washers so you'll have one for the other valve. Replace the washer and reassemble the faucet.
   
2. Around the handle
   If you see water coming from below the handle, the packing nut is leaking. Older faucets have a string-like graphite packing material wrapped around the stem. Newer faucets use an O-ring. First try tightening the packing nut clockwise... about one-half turn. If this doesn't stop the leak, remove the packing nut and replace the packing or O-ring; then reassemble the faucet. If the valve is using the graphite packing material, it might be a clue that you should shop for a new faucet.
   
   
3. Between a pivoting spout and the body
   The spout might be held in place with a packing nut, similar to the faucet stem, or it might have a nut at the top of the spout. In either case, remove the spout and replace the packing material or the O-ring seal. Then reassemble the faucet.

Single lever faucets also are known as "washerless" faucets. They are easier to repair than compression faucets after you determine what type of faucet you have. There are three types of washerless faucets: ball, ceramic disk and cartridge.
Leaks are evident in two places... dripping from the spout and seeping from around the spout where it joins the body of the faucet.
Leaks from the spout indicate that the ball, disk or cartridge is leaking. To repair, turn off the water to the faucet, then remove the handle. The handles on ball-type faucets are held in place with a setscrew that requires an Allen wrench to loosen. Ceramic disk and cartridge-type handles usually are held in place by a screw hidden beneath a cap.
On ball and ceramic disk-type faucets, remove the ball or disk and replace the seals. You can buy replacement kits for these faucets at the hardware store or home center.
On cartridge-type faucets, remove the spout and pull out the retainer clip that holds the cartridge in place. To remove the cartridge, pull on the cartridge stem with a twisting motion. If it resists, install the handle so you can a better grip on the cartridge to pull it out. Take the cartridge to the hardware store or home center and purchase an exact replacement kit.
Reassemble the faucet according to directions.
Leaks at the spout-to-body joint indicate an O-ring failure. Disassemble the faucet as described above. Remove the spout sleeve and replace the O-rings. It's a good idea to replace these seals if you have the faucet disassembled for repair of the ball, disk or cartridge.

Jado are ceramic disc cartridges no washers you should replace both sides.You need to remove the handle and unscrew the cartridge

It is a rubber gasket that is leaking, Pull the cartridge with a cresent wrench. There will be a paking nut on the top of the cartridge where the handle connects. You should be able to remove this with a pair of pliers. There will be a rubber o-ring inside. Take that to the hardware to to find a replacement to it. It wont be hard to match they keep tons in stock at ace or lowes