Quoted from Markharris2000:That's a weird problem. Axial capacitors are pretty mechanically sound once installed. The two axial wires physically hold the 'can' tight once soldered. If the capacitor can 'fell off', I suspect it was damaged in manufacturing or assembly or previous user work (after it was soldered in place, something hit the top of the can pretty hard and pulled the wires out, but the plastic kept the can in place when visually inspected) --- the capacitor was likely NOT functioning at all. The node board was likely behaving as as if there was no capacitor installed. Easy to clean the old axial wires out of the holes with a solder sucker, then drop in a new 470u/16v capacitor and consider it a professional repair.
Note: The RED LINE on the edge of the can usually indicates "NEGATIVE" polarity, even though it is printed in RED ink! See: https://www.digikey.com/en/blog/identifying-capacitor-polarization
I agree there was likely some overt damage, and that capacitors don't usually fall off by themselves.
But just a nit: the capacitor pictured above is a "radial" capacitor. Axial capacitors (which are also very reliable mechanically IMHO) are the ones where the leads are aligned through the center of the component, one at each end. See e.g. https://en.wikipedia.org/wiki/Capacitor#Styles