Most definitely, Yes. All kinds of thermal compounds have a shelf life. Depending on the material, a thermal paste can expire in 3-5 years or even less if it is not stored in optimal conditions. Although, this lifespan depends largely on the kind of thermal paste you are using.
 
  Applying thermal paste as a means to mount your CPU cores heat sink will absolutely outlast any pad placement and will be a much sturdier option in terms of wear and tear.

OP is talking about thermal pads not paste. The green ones that come with EVGA cards last like 2-3 years and they'll leak oily fluid all over your graphics card's board during those two years. It can cause it to rust.

Armons account
Most definitely, Yes. All kinds of thermal compounds have a shelf life. Depending on the material, a thermal paste can expire in 3-5 years or even less if it is not stored in optimal conditions. Although, this lifespan depends largely on the kind of thermal paste you are using.
 
  Applying thermal paste as a means to mount your CPU cores heat sink will absolutely outlast any pad placement and will be a much sturdier option in terms of wear and tear.

What? There are pads out there that will last damn near forever, they're made of carbon, they've been with us for a while. LTT has a few vids on them. And thermal paste HAS to be reapplied after some time because of the heating and cooling cycles of your CPU, the metal expands and contracts, and what people mistake for "dried" thermal paste isn't "dried." It doesn't actually dry out, ask Der8aur about it, anyhow, it's just the CPU itself squishing out the thermal paste. I would def reapply thermal paste after a year or something along that lines, and if you have a really loose thermal paste, I'd replace that even sooner. Even the big thermal pads like 2mm and 3mm that people are putting all over their VRAM so they can mine ETH will last for at least like 3 years, though I can't speak how long the absolutely terrible ones that Gigabyte uses in their 3080s... what I can say is that replacing those pieces of **** with better ones was the difference of nearly 35c... But pads are not subject to the squishing effect that pastes are. The IC carbon thermal pad will last there in between your cpu and cooler for your entire life. So ya maybe the paste doesn't actually deteriorate like certain pads do, but it definitely needs to be reapplied more often than a pad.

I never really considered that thermal pads can wear out over time. Thermal paste, yes, but thinking about thermal pads is new to me. I think if you *are* going to replace your thermal pads, definitely make sure you match the height with the original pads so that you don't end up cracking the GPU die because the thermal pads were too short.

EVGAuser145
... they'll leak oily fluid all over your graphics card's board during those two years. It can cause it to rust.

Silicone oil can cause rust?  That's very peculiar.  I disagree.

knightostjohn
If you're looking for top performance, you could upgrade your thermal pads to these:  https://www.amazon.com/dp/B00ZSELP3O/?pldnSite=1
They have a thermal conductivity of 17W/mK. Normal thermal pads are usually around 1 to 5. I'd think these would last longer too. They're not gummy like others.

W/mK means nothing. There is no standardized way to measure W/mK, so the advertised W/mK between different brands cannot be compared and means nothing.
Personally, I don't like Fujipoly pads because, contrary to what you said, they are mushy and fall apart if you take the cooler back off. This makes them only usable one time, usually. Since I haven't seen considerable actual performance differences with Fujipoly's ridiculous advertised W/mK, I look for cheaper firmer pads which can often be reused.

Not necessary shelf life, but shouldn't be used and reused over and over.