However, as the time went by, I couldn't but feel my dream disappearing little by little.

little 的意思是"小的、少的"，在这里表示"少量"。 by 在这里表示"通过...方式"或"按照...顺序"。 little by little 是一个固定短语，表示"逐渐地、一点一点地"，用来描述缓慢渐进的过程。