How long is the life of a shot of espresso?
This barista says no, you can enjoy your shot for a little while:


  In reality, there are only a couple of things that happen to espresso
  over the course of a few minutes.  First, the crema or foam that sits
  on top of the espresso reintegrates with the liquid.  Crema, on its
  own, contains some of the best flavors and aromatic qualities of the
  espresso in high concentrations.  Drinking it straight can be
  overwhelming but, it stands to reason, that having the crema
  reintegrate might actually be a good thing.  Second, the espresso
  cools down.  The temperature of espresso has a lot to do with how we
  taste the various flavors contained within it...


I am not an espresso fan myself--I like regular coffee, but not after it has cooled down, and never reheated.  Many folks are perfectly content to microwave a cold cup and drink it.

I imagine that older, colder espresso is palatable to you to the extent that you are willing to tolerate it.  A small shot of coffee--and lets face it, that is all espresso is, even if it is brewed in a fancy manner--is going to cool off much more rapidly than a full cup, or a full pot.