Accelerating on the 2nd gear and hitting above 5000rpm, the engine starts fading (similar behaviour as to when you have run out of petrol). To overcome this problem and ensure I don't breakdown in the middle of the road whilst travelling 40-50km/h I have simply been shifting to the third gear which accelerates to 4th and 5th just fine. It's the second gear that is experiencing acceleration problem. Any thoughts? I'm thinking this is a common problem seen in old mnotorbikes??

You do not say which model you have . I think you are dealing with Kei Hin carburetors that have floating vacuum pistons ( not the rubber diaphragm style). In this style piston the aluminum piston floats in the carburetor top up and down about 3/4" or so. It is a once or twice a year tradition with this style carburetor (used on older GL1000, GL1100, and CX500's) to remove the top, pull out the piston, and clean both the inside of the carburetor top and the out side of the piston thoroughly with carburetor cleaner. This is so they do not stick or hang up during normal operation. When the carburetor top sticks on one or more of the cylinders it will cause a flat spot in the acceleration curve like the one you describe.