Somewhere out in space, we stumble upon an alien device. It is immediately taken back to base or Earth or wherever and given to scientists to investigate. Reverse engineering the device reveals that it's fairly simple to duplicate, and it can be used to greatly simplify some process (in this specific case, FTL transportation), but the scientists are completely baffled as to how the device is able to do what it does (and in fact, all records indicate that the aliens discovered how to build it by accident). The people in charge of the operation aren't phased by this, however, and immediately begin mass production of the device.
How long, depending on the complexity, is it reasonable to assume that the physics behind such a device could go unexplained? With the whole human population—and specifically, all human entrepreneurs—exposed to fully operational replicas, I can't imagine it would stay this way for long. But what if I made tampering with the device to set up scientific tests difficult (e.g. remove or modify any one piece and it won't start) or dangerous (e.g. add another wire for debugging and turn it on and suddenly your insides are your outsides)? How impossible or fatal (or both) would I have to make it to have the device stay unexplained for 50 years? 100 years? Indefinitely? And how would this affect its use or marketability?