Some unsolicited solutions, maybe not for you but somebody in a similar situation: maybe replace it with a supercapacitor (needs some wiring changes, otherwise it won't ever be charged, should last long enough for most power outages), or use a stack of coin cells in parallel (difficult due to physical dimensions, and they'll still go dead at some point). You can also short two wires on the ATX supply to automatically turn on the computer when power is supplied (which may not be good enough if you have to press a key during boot to dismiss the low battery warning). Or hack the BIOS :)
That issue doesn't apply to supercapacitors (nor to any capacitor manufactured in the last 15-20 years, really). It affected some aluminum electrolytic capacitors manufactured with a defective electrolyte in the early 2000s.
