Do SSRs need to be heat sinked?
While not a requirement for light duty applications, a must for continuous duty with medium to high power.
The coil of a relay is rarely, rarely, rarely ever the failure, unless you are using the cheapo "12 volt RadioShack 20 amp relays"
or it is defective to begin with. I assume your servers are in a temperature controlled environment, so excessive environmental heat shouldn't be a concern.
.....Besides, it sounds like you are looking for a way to shut off power and bring it back up from a control computer. Being that this is a controlled shut down system, why not use NC relays and have the energized coil OPEN them, this way the coil isn't energized but on occasion. Just an idea....
Mechanical relays usually fail after repeated contact arcing from cycling, they become pitted. As he said earlier, static duty isn't likely to cause a failure, though sometimes a defective contact point with a tissue-thin gap will cause trouble, but this is unlikely as well. (That's why you stay away from RadioShack).
SSRs OTOH have their trouble as well. I am QUITE familiar with SSRs in high power control circuits, especially temperature control. It is one of the more common replacement parts that I have to keep on hand. This of course is round the clock cycling with 20 amp circuits, but they do fail. Heat sink compound can get dry and ineffective over time. Surges, combined with power converted to heat, combined with time, will eventually do one in. The one good thing about them is precision control for systems that cycle at high frequencies. A mechanical relay wouldn't last two weeks in the circuits I work with. This doesn't sound anything like your application.