The thing which causes otherwise sensible people to be afraid to ask for something, while asking for that something is appropriate at the given situation. Although there are good chances of receiving an agreement, the mere possibility of being rejected (and receiving the emotional downer along) scares the person away from taking the risk.

So, let's do the "risk calculation":

  • Don't ask = unconditionally keep the inconvenience of not owning the thing you need.
  • Ask = either get what you want and stop the inconvenience (and get a gratifying sense of success as well), or get rejected and experience a short-paced emotional "downer".
The choice is clear, but it's only so in the rational consideration. Thus, this fear could be often classified as a phobia.

That's somehow similar to a rationally-thinking person being afraid of getting an injection. (S)he recognizes the need for the vaccination, and knows the pain inflicted by the needle is small and short-paced, but the anticipation of pain frightens much more than the actual injection.

Fear of rejection often prevents people from advancing or acquiring whatever they want (a significant other, a friend, a raise or a better job position etc.). Getting over it (along with stage fright, low self-esteem etc.) is considered a step on your way to success, and gets covered by way too many "How To Win Friends And Influence People"-style books.