Howdy Mark,
ahhhhh the old 1906....and one of my favorites...
Ok possable problems.... check the extractor and make sure it's getting a good "hook" on the case rim.. you can do this be breaking down the gun and watching from underneath , when you move the bolt back the extractor hook will slide up and catch the rim of the cartrage.. the springs in there are hell for stout.. but it's possable that "gunk" has gotten into the cutout for the extractor and not letting it do what it needs to do.
cure break down the gun,, and scrub the bolt get all the old gunk out.....lol
second possability.. check the end of your barrel... theres a cutout alongside of the chamber where the extractor rides on it's upward movement..also a great place to catch lead and other nasty fouling and may be keeping the extractor from getting a good bite on the case
third possabilty.. the gun has been fired using either shorts or longs ( can you even find longs anymore?) and has devloped a carbon ring in the chamber causing sticky extraction...
fourth... going along with the sticky extraction..... the old .22's use to be blackpowder.. which did nasty things to steel.. it's possable that you might have pitting in your chamber..and when you fire a shell it's expanding enough to be catching in the chamber...
you might try using a brass brush mounted in a drill.. and lightly trying to burnish the chamber
last case...and it doesn't sound like your that far..but ,is to reline or rebarrel...and for a "generic reference". most all parts from the models 1890, 90, 1906, 06, 62, and 62-a from the same production time frame will interchange.
and replacement barrels are avaiable from gunparts....total cost about 80 bucks and a half hour time.....