Most of the time while riding my motorcycle gear changes down no neutral from second on it's own even if I shift it with full clutch. And sometimes the gear acts as if it is neutral when it is above 3rd gear. This happens very rare but still it is a problem. In both the cases I have to shift gear again. What could be the issue? I am replacing engine oil periodically.
Given this happens in multiple gears and specifically while accelerating, I would check first for clutch slippage. What sounds like is happening is your clutch isn't grabbing when you let it out on acceleration, and so is slipping. The causes for this can be the wrong type of engine oil, if your bike shares oil between the engine and clutch (car oil reduces friction more than motorcycle clutches like), not enough slack in the clutch cable, or burned-out clutch plates-- I'd check for all of those.
Additionally, if the clutch has been slipping then regardless of the initial cause, there's a pretty good chance your clutch plates are glazed either way. You can try sanding the glazed portion off or just replacing them after inspection.