Got any failed parts? Take 'em apart and see (mind the goopy oil; not a hazard, just messy, they haven't used PCB in DECADES, even the cheaper countries know better than to touch the stuff... I think?..). The large current sounds like a good way to melt the connecting straps. Note the internal construction is a foil-film jelly roll with a couple tabs crimped into it; the tabs are just floating in air, headspace above the roll, before the sealing plate and terminals. Or maybe they're immersed in oil, but the power dissipation won't be much better in that case (very little circulation).
As a matter of design review -- mind, not knowing anything about what this is, other than, I guess, some manner of mains inverter -- it sounds like inappropriate type capacitors were chosen, perhaps simply because motor-run types seem familiar enough for mains use, or are cheap and abundant; but I would consider several points against them, the fairly weak connections for one, but also the large inductance of same (figure >20nH per cap, plus wiring!), the low frequency range (intended 60Hz use only), whether MFG has any data on higher-frequency operation (almost certainly they don't provide a V or I vs. F rating/plot), and whether shopping revealed any better/more suitable alternatives (axial tape-and-fill, and boxed style, esp. X1/X2 type MKP, are much more likely to handle the current and frequency, and aren't particularly expensive).
I also don't know whether this is actually a design scope question or repair/maintenance, but it at least seems likely that attention should be brought to the designers if nothing else. Maybe it's also very old and that's N/A, I don't know.
Tim