My brake pedal sinking when I hold it long. I kept refill new fluid every 3 days.
I couldnot find any leak in front or rear brake. If Master cylinder's fluid leaked into booster, can the fluid damage the booster ?

 

Yes it can... Did u check at your break peddle where the rod pushes into the master cylinder?? any weaping around there?

 

Could be just an internal leak in the master cylinder like a damaged seal. Try bleeding it to see if it changes anything. Just don't press in all the way on the piston until it bottoms out. That will damage it, if it's not already.