Rotary valves on a French horn have exceptionally narrow clearance between the rotor and the valve casing. Any sediment or build up of gummed lubricant or minerals, or warping of the rotor or casing will freeze the rotor in place. In most cases, it's impossible to know what has caused the valve to freeze, so it's important to be cautious and gentle in your attempts to unfreeze the rotor; it's easy to cause damage to the rotor or casing, which would require expensive repair.
Loosen the tiny screw on the stop arm and unwrap the string which operates the lever mechanism. This deactivates the lever: Pushing on the lever to loosen the stuck valve is likely to break the string or bend the lever.
Remove all crooks and tuning slides from the horn.
Remove the valve cap and cover the centre of the valve inside with several drops of rotary valve oil. Replace the valve cap. Rotate the horn until the valve slides casings extending from the stuck rotary valve are facing up. Squirt valve oil down the centre of the shortest of the valve slides, taking care not to allow the oil to hit the sides of the slide casing on the way down. Unscrew and remove the screw at the end of the stop arm, squirt valve oil into the threaded area and replace the screw. Wait 10 minutes to allow the oil to work its way through the valve. Wiggle the valve again, then again try to rotate the stop arm around the stop arm hub. In most cases, repeatedly attempting to move the stop arm, and, once it moves a bit, moving it back and forth in ever-widening arcs, will eventually result in a smoothly-working valve. However, if this doesn't work, go on to Step 4.
Place a thick bath towel in the bottom of a clean bathtub.
Fill the tub with 1 foot of warm--not hot!--water, adding a drop or two of dish detergent to the tub as it fills.
Place the horn gently on the towel in the water; allow the horn to rest there for up to 30 minutes.
Remove the horn from the tub, draining all the water from the inside of the horn by rotating the horn several complete turns over the tub. Dry the horn with a towel.
Attempt to move the valve while the horn is still warm from the water; grasp the stop arm between your thumb and forefinger and wiggle it gently, then try to pull it around the stop arm hub. If it will move, stop manipulating the stop arm and lubricate the valve as outlined in Step 1, then work the oiled valve until it moves smoothly. You don't need to advance beyond Step 8; re-string the valve and replace the valve slides and crooks. Your horn is ready to play. If the stop arm hub still won't move, however, go on to Step 9.
Assess your horn and your situation. The next step outlined below could conceivably cause damage to the horn, although it's not likely. Bring your horn in to an instrument repair technician if it's an expensive or very valuable horn. If, however, it is urgent that you get the valve working (for instance, you have an important gig coming up and no time to get a technician involved) or if the horn involved is not particularly rare or valuable, you might wish to proceed to Step 10.
Pour about a tablespoon of kerosene into the valve casing, and place a drop or two under the valve cap. Allow the kerosene several hours or overnight to work its way into the valve and dissolve any gummed lubricant in the valve. Try to move the stop arm again. If the stop arm still won't move freely, you should take your horn to an instrument repair technician.
In nearly every case, a frozen valve will work lose with lubrication and gentle, persistent manipulation of the stop arm with your fingers. The gentle, patient approach is the most effective, and it won't damage the horn. Most often, valves freeze when a horn has been stored, unplayed, for weeks or months. Rotary valve oil evaporates quickly, so if your horn will be in storage for more than a couple of weeks, take it out weekly to add oil to the valves and work them briefly. Sometimes, oxidation will form on the rotor of a newly-cleaned horn, causing a temporary obstruction in the valve. Valve oil and patient working of the stop arm are again the solution.
Don't attempt to remove the valve from the casing. This can result in further damage to the valve, and should only be done by someone with the right tools and expertise.