Government shutdowns actually happen quite a bit, and in no way does it prove that the Civil War never ended. The Civil War did end or we would still have troops fighting against each other in our own country. This does not happen and therefore there is no war. No war means there is peace.
A government shutdown shows that our bipartisan system is not currently working, but the Civil War was officially over more than a hundred years ago after the Confederate States of America surrendered and were re incorporated in the United States. I firmly believe there are no parallels between the two events.