While I don't have "engineering degree," I do have many years of experience with the Davis line. For me when my ISS was doing exactly what yours did, I actually fiddled with the board and was able to remove the old cap from the board by heating with a low volt iron , the solder. then bend the leads and insert them into the former holes and re soldered, trimmed. I even put a little cushion between the super cap and the board as Davis suggested.
I found it odd that so many of these tend to fail, originally I thought Davis bought a bad lot, then I realized they were cheap. Anyway, lacking the engineering expertise, I used common sense, and fixed it.