If the problem is not fouling, it is most likely barrel heating. That type of rifle was made primarily as a hunting rifle, where only a few shots are ever fired at one time.
You can test this by repeating the firing without the magazine tube, loading the rifle as a single shot and resting the receiver, not the barrel, on sandbags. If it keeps its accuracy, the problem is not fouling.
On that rifle (and the Winchester as well) the barrel is usually pretty tightly bound to the magazine tube. When the barrel heats, it tries to expand lengthwise. If it can't, then it warps enough to cause inaccuracy. (Remember the cuts in the stock of Mauser military rifles to allow the stepped barrel to expand without contacting the stock?)
A good gunsmith can relieve the binding at the proper places without having the rifle rattle.
Jim