I've had 2 H&R's, a 30-06 and a .243, the 06 shot great (but needed a trigger job in a serious bad way), I could shoot beer cans at 400 yards on a regular basis, and after a while the accuracy left the gun, could have been sevral reasons.
The second was the .243, it was trouble from day one (2nd hand gun), it would break open after a round was fired from it, or it would misfire.
you could hold the gun up to a light and wiggle the sock and forearm and see the light shine thru the barrel/reciver, ther was just enuff slop between them that the fireing pin couldnt make propper contact with the primer hence the misfire.
The breaking open was caused by the slack also, just enuff slack that the locking mechanisam wasnt tight enuff to work correctly.
I solved these problems with a piece of shim stock wrapped around the hinge pin (what the barrel pivots on), it fixed it but I dint like the idea of it.
After a lot of diggin around what I found out was when the round fires all the presure is put on the hinge pin, an immence amout of presure at that, and (if I remember what I read)the pin can bend ever so slightly and cause the gap between the barrel/reciever, just a few thousanths of a inch can create accuracy problems, if ther is room for the case to move backwards at the firing of the round its aint gonna be accurate.
A bolt gun locks up good and tite, no room for the cartrige to "back up" when fired, hence it makes it more accurate, but I love a single shot rifle myself, but the next one mite be a Ruger no1.
Just say'n. (because a unaccurate gun just stinks, aint fit to build a fire out of)