Manoj's small battery fan has become slow

Why

Manoj has named the most likely cause, and starting with the likeliest is good thinking, not lazy thinking. The trouble is that 'runs slow' is a symptom several different faults produce identically: a weakening battery, yes, but also loose or greenish corroded contacts, a bearing stiff with dust, or a blade quietly rubbing the guard. From the outside all four look the same. Test: put that same battery into another device. If the second device runs perfectly, the battery has just been cleared and the fault is in the fan. Bhavna is right: when several causes produce the same symptom, the honest position is 'I need one more observation' — and usually one simple test separates them.