200V DC rating is not enough, despite 120 VAC having a peak voltage of only 169 volts.
AC does make things worse, by rapidly repeated severe voltage swings combined with some development of heat.
The capacitor needs to have an actual AC rating, and one that includes your AC voltage with a comfortable safety margin. If it has a DC rating, chances are that will be around 400 volts DC. And not every cap rated
400 VDC is dsafe for use with 120 VAC, even if non-polarized.Preferably, it should be "UL recognized" or the like, for some assurance that it is reasonably reliable against failure, or at least an unsafe failure.
Back in the early 1980's, in an experimental sodium lamp ballast, I have blown an 800VDC cap and two 600 VDC ones with 240-260 VAC 60 Hz with less than 10 operating hours of this combined among the three of them. One of those capacitor blowups was a spectacular one that left a major oil stain on the ceiling above. I learned the hard way that actual AC ratings are required here.
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One more thing: If there is a switch upstream of a capacitor across a power line, then the switch may be in for severe contact pitting.
Then again, I doubt a voltage spike lasting long enough to burn out a transformer will be absorbed by a 1 uF cap across a 120V AC line.
I would lean to looking for intermittent overload by the transformer's load, the transformer's load intermittently drawing a large amount of DC (such as by failing-open one diode in a bridge rectifier).
Or, the transformer being connected incorrectly.
(Such as a 120V/240V one with 2 primary winding sections needing both primary sections to be connected in parallel with each other for full power handling at 120V, but only 1 of them is being used.)