What brand of 1860?
Did you buy it new? If yes, this may be warranty issue since nipples should not flatten down that fast...
If a used gun, may have wrong nipples, hammer nose may come too far forward, mainspring may be way too heavy, or a combination of things. Most of the replica cap & ball revolvers have mainsprings that are way too strong and really hit hard.
I like to lighten the mainspring and/or place a homemade leather "washer" between the mainspring and triggerguard on the Colt styles.
(Sidebar Note: The Ruger Old Army is so precise that it may be dry fired without damage to the nipples as the hammer does not come into contact the nipples)
If you have access to a lathe or drill press you could turn down the nipples with a file and sandpaper and reuse them.
If you can diagnose the cause that will help solve things... might help to buy high quality nipples with better steel.
Please post what you find out.