A few weeks ago I bought a Remington 40X 22lr rimfire rifle. It is a rifle that was sold through the CMP, and as expected the rifle looks beat on the outside,dents, scratehes, and the signs of heavy hands in storage. On inspection of the bore with a bore scope the barrel looked good. I test fired the rifle using both match ammo and Federal Champion (510) ammo that has proven to be very good in my other rifles. I was not impressed by the accuracy. Backing off the two barrel pressure screws in the forearm helped some with improving accuracy. Then I noticed that the firing pin was bent and worked on at one time. A trip to Remington Arms in Illion NY was made and a new firing pin was fitted by the Custom Shop. Now the bolt lifts hard and the rifle has a miss-fire once in a while. When it does have a miss-fire it will discharge on the second strike of the firing pin fall. I have looked over the bolt and the pin assembly and can't find burrs or a reason for the heavy lift. I would be interested in hearing what other users of the Remington 40X Rimfire rifles have to say about their rifles and what is going on with the one that I have.

correct me if i'm wrong (i[m sure somebody will) but the cmp 40x rifles our club had we got in the late 1950's, thus I would expect that you should check the stock bedding & Probably glass it. also it's probably had lots of ammo through it and would require a really good cleaning (which i presure you have done) i thing you need to find a good remmy smith and forget the factory dubs.

I agree with Butchloc.
Disassemble every part you are comfortable with and clean them. Scrub the bore, then check the crown to see if it is smooth without damage to land/grooves. Lube every thing lightly, including the sear, and reassemble. At 25 yards fire 10 rounds and the hole made should be under 1 inch using any good 22 ammo. Glass bed the front of the action and about one inch of the barrel (the rest of the barrel is free floated), repeat the ten shot string, and you should be at 1/2 inches, or less. If not, its you.
The Rem 40X is one of the all time acccurate .22 rifles.

As the other guys said, it sounds like it has had a long run, meaning lots of rounds. After a good cleaning you might want to try a box of Eley Tennex, or the new stuff from RWS( I think the name has changed). Good luck