I have been growing this alpine for the first time this year. It
produced a flush of beautiful blue gentian coloured flowers. These have
now finished and the leaves which was a healthy looking green has now
turned black and died. There are some new green shoots arising in a few
places encompassing some new flower buds, so I know the plant is still
alive. But should the old leaves that came with the first flush have
died so quickly or is that normal for this plant?

"Frank" wrote
I have been growing this alpine for the first time this year. It
produced a flush of beautiful blue gentian coloured flowers. These have
now finished and the leaves which was a healthy looking green has now
turned black and died. There are some new green shoots arising in a few
places encompassing some new flower buds, so I know the plant is still
alive. But should the old leaves that came with the first flush have
died so quickly or is that normal for this plant?

It is a lovely shade of blue, isn't it.
Have you got an alkaline soil? Lithospermum or Lithodora diffusum
(they're synonyms for the same thing) apparently like a soil neutral or
on the acidic side according to the RHS site.

I've got one of these flowering now in a pot and like yours has new
green shoots at the end of stems but it's got somewhat straggly and dead
looking in the middle. I think mine's probably suffering from the water
being too limey and hard hereabouts. Pity it didn't state it's an acid
lover on the label or I'd have potted it in an acidic compost.

--
Sue