Star Jasmine leaves red and falling off – will it survive?!

I bought two of these star jasmine plants recently, they’re on our SW facing balcony and get lots of full sun.

The leaves were red when they arrived and are now falling off (same of on both plants – I won’t buy plants online again!). The few new buds that were alive when I received them are dying and falling off too. But there is new growth coming up form the bottom.

Do you think the longer stems will survive? Will new shoots grow from them? Or should I cut them off and just focus on the new growth?