The buffer is an outer casing/housing, with tungsten weights in the housing (casing) to act like a dead blow hammer and the end urethane bumper held in with a roll pin.
At what location did the buffer break apart?
Is the end bumper being chewed up by something in the end of the receiver extension, and what type of buffer are you using. Is it the BB type or tungsten weight type, the standard car buffer, or the plastic ended 9 SMG type.
Bottom line is in order for the rifle to recoil the buffer hard enough against the back of the receiver extension would require the ammo to be loaded hot as hell, But the rub to this that when the ammo is too hot, the case sticks in the chamber due to the higher pressure. This leave three areas to check on the rifle. The first would be the buffer itself, the two may be cheap parts that are defective. The second would be the recoil spring, which may be weak or clipped. The last would be the bolt lock up, or lack of that is causing the problem.
Also, are you sure that your stock uses the shorter car buffer, and not the full-length size? Using the wrong buffer would cause free run for the buffer, and the carrier key to slam into the back of the charging handle, which leads to a cracked receiver.
If possible, post a photo of the broken buffer so we can get an idea of the breakage, and what may be causing the problem.