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If you bought a new set and used those 'new' clips to install them, that was your mistake. The new clips are non-hardened JUNK and will not stay in position. When I first saw them, I threw them in the trash; then cleaned up the old ones and resused them. No problems.
There is just not enough (or any) spring retention with those new clips. Since you no longer have the originals, you may want to install those clips, then find some 'tab' on them somewhere to bend for permanent retention of that clip. Unfortunately, that clip will still allow the cylinder to wiggle around [even if you do bend it to retain it], as it has little, if any, spring load to keep it solid.
P.S. I cannot understand why vendors sell this crap. What would it take to have the manufacturer replace these with decent pieces...or just harden the ones they are presently sending so that they will actually WORK!
Just make sure they have enough spring in them to keep the ear in the hole. If you look at the clips real close you'll see they have a tiny ear at one end. The cheap lock sets come with new retainers and the curve sometimes isn't enough so bending them just a bit extra makes sure the retainer ear stay's put and if this happens they will not come off.
Those look just like the ones that came with my new locksets (different vendor...but may be the same manufacturer). And mine did not have ANY spring effect at all; they merely had some resistance to bending due to the strength of the metal. And I stand by my comment that they [at least, the ones I got] were JUNK!
If you have a 'loose' one laying around, try to bend it (relatively easy); then see how much the part wants to return to its original shape. My guess is that it would be about.....zero. If so, it is useless and should not be included in the shipment. It would be more of a service to customers to include a note on how to re-use the original clips that were removed.