I Have A Hanging Fuschia Plant And It Is Losing It's Original Flowers, But Doesn't Seem To Be Bearing Many New Buds. How Can I Help It?

This could be due to overwatering and the roots are rotting and drowning. If you have been overwatering, let the soil dry out a bit - hold off watering.

The soil could be too compacted and suffocating the roots.

Check for spider mites or mealy bug and if you see any on the plant spray with detergent.

Pick off all the dead flower heads, including the bulge at the base (which will be forming seeds). Plants won't continue to flower after forming seeds, so you need to kid it that it has not succeeded in doing so. Then give it a good watering with added flower fertiliser to the strength recommended. This should get it going again.