Are you sure they remained "very Christian"? I recall some of them were Arian Christians, which was considered a heretical form by the Catholics. The Vandals declined under the rule of Huneric, the Byzantines under Justin, and Burgundy under Charles the Bold. Spain overextended itself in creating its empire (as did the British), but it has survived (so far). I am unsure why you included the Franks and Austria-Hungary.
Actually if anything Christianity was a bad thing for the Romans, Their empire lasted ~1100 years before Christianity and after Constantine converted the empire to Christianity the empire fell apart within 140 years.
The cause of the fall of Rome is widely contested. Gibbon blamed it on Christianity, but most modern scholars disagree. According to Weber, Christianity was part of Rome for its last 400 years (where did you get 140?), which led him to assert that four centuries was a long incubation period for a fatal illness, especially considering the rise and fall of the British Empire spanned only about 200 years. It is also worth noting that Christianity had lost some or most of its influence near the end. Pirenne blamed the fall on the rise of the Islamic faith in the east during the 7th and 8th centuries. Some even stated the Empire never really fell, but was transformed. But the most prevalent theory for the downfall appears to be economic in nature. Rome, like modern America, built a unsustainable welfare state (a welfare state is socialism, not Christian).
The "140" years comes from the time Constantine made Christianity the official religion of the Empire in the mid 330's to Rome's fall in 476. I won't solely blame Christianity for Rome's fall but it did play a part, Multiple civil wars between groups of Christians weakened Rome's central authority which made them more vulnerable to the Huns and Vandals. Also because the Visigoth's were willing to convert to Christianity the Romans allowed them to immigrate into their territory, A devastating mistake and one Battle of Adrianople and sack on Rome later the fall was inevitable.
A side note about Constantine: I find it very ironic that Christianity which is supposedly a pacifist religion and a religion of the poor gained prominence because a rich and powerful emperor saw a cloud in the sky and believed it was a sign from God to kill people. I guess he read too much of the Old Testament.