Budgerigar hens may often throw out the eggs they’ve laid, and for several different reasons. Basically it is the budgie’s way of saying, “I don’t want to waste any more time on this egg”. This can happen because they believe the egg is defective, or infertile. The bird may also have noticed human scent on it. It is extremely easy for a budgie owner to accidentally leave its smell on eggs and terminate the laying process, making it important to avoid handling the eggs with bare hands.
Look over the eggs that the budgie has thrown out. Look for defects in the egg. A hen will throw out strange eggs because it doesn't want to waste energy on eggs that won't hatch.
Place a small desk drawer or a box of similar dimensions inside the laying area. The high sides of the drawer will prevent the hen from pushing out the eggs. Wear gloves when handling the box to avoid leaving your scent on it.
Fill the drawer with used clothing to keep the eggs warm. Place the laid eggs in the drawer. Again, wear gloves to contain your scent.
You could always buy an incubator to hatch the eggs yourself – or, better still, find out how to build your own!