After my buddleia come into leaf this year, the shoots curled up and fell off.
I am pleased to say,there is now new growth growing up from the base.

How can I prevent this happening again?

The main branches of your buddleia appear to have died, cut the plant down to its base, leaving the strong new basal growths.

Buddleias generally respond to regular pruning.

Each year in March / April, cut the branches back close to their base, and this will encourage strong new growths to develop and flower in late summer.