If a little bit of chromsome comes off, does that cause problem for fetus later in life?

YES! The concept of "a little bit" of chromosome is faulty to begin with; even microscopic chromosomal deletions can have profound health effects (or even be lethal). Depends on what proteins that chromosome was coding for and how large the deletion is. Sounds like you could benefit from comprehensive genetic couneling.
Chromosomes. What is "a little bit"? Lack of some chromosomal material may be associated with an unbalanced chromosomal complement. That is not normal and depending upon what chromosomal material was lost may affect the way the fetus develops and functions.