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First, Putting the hammer in the cocked position is engaging the sear..that is the way it works...next Who said to do that? factory manual? I have the Gun Digest of Firearms Assembly and Disassembly Part III Rimfire rifles and your riflke is listed under Sears Model 31 with the discriptive paragraph staing it is a High Standard marketed by Sear using the JC Higgins tradename..point is this book doesn't say that. The only special instruction does concern the trigger group but has to do with reassembly of the trigger group itself and not the replacement of it into the stock...however cocked with the safety on is a normal procedure for such an assembly..That said..I would suspect that your problem is with the bolt and its rearward travel..it is this that re cocks the gun after it is fired..if it doesn't travel far enough to the rear..then the math is wrong and the hammer doesn't rotate far enough for the hammer to re-engage the sear. However..there is a set of parts at the rear of the trigger group involving the hammerspring and the hammer spring guide rod..if there is an issue here..improper intstallation of parts or detrius build up..then hammer travell will be affected..BTW did you disassemble the trigger group ior the bolt assy?
On the right hand side of the trigger group, there is a music-wire spring that must fit in the slot in the linkage arm (straight above the safety).
I have had the trigger group drop out when I removed the cross screw, and impact on a carpeted floor is enough force to pop the spring out of the slot.