I have had some problems with some old & new P08's that ended up being poorly cut/ rough chambers.
On the old guns the chamber was sometimes too rough and the casing would drag on the way out causing a jam on the next round and the failure to pick up the next round
On new guns like the stainless ones the chamber was way too tight and using a "new" finishing reamer would correct all problems with the functioning of the gun.
Some Questions for everyone: I don't know the answers- not for sure

1) Is there a difference between the brass used in the 40's and now?
2) Could it be that the new powders create too much pressure even though within modern limits?
3)Is the bullet crimping different than used or perhaps tighter?
4) Could primers be an issue, the pressure curve inside a casing varies greatly depending on the primer and this could cause sticking of the case on the back end on a tight chamber?
When you consider that "newly" created lugers have functioning issues even the HK's then something else is going on!!
Just some things to think about
Vern