Is there a word for the "call of the closing door" / "closing opportunity"?

Solution 1:

I think the expression seize the opportunity: may convey the idea: (from TFD)

• take advantage of an opportunity when offered.

  • My uncle offered me a trip to Europe, so I seized the opportunity.
  • Whenever you have a chance, you should seize the opportunity.

also the sayings:

• leap at the opportunity (to do something) and leap at the chance (to do something);

• jump at the chance (to do something); jump at the opportunity (to do something)

As for a term to define the sense of urgency to seize an opportunity : (from Wikipedia)

• Fear of missing out or FOMO is a form of social anxiety, whereby one is compulsively concerned that one might miss an opportunity for social interaction, a novel experience, profitable investment or other satisfying event.