I think you have a problem.

H. corsicus or H argutifolius as it is now known is not summer dormant. You should have about 24" of new top-growth.

The flowering stem will normally die back and wither, but this should be replaced at the same time by new growth that will bear next springs flowers. Best actually to remove the old growth when it begins to yellow as a precaution against blackspot.

It likes full sun and good drainage, It will not be very happy in shade as it will grow too tall and collapse, also has an aversion to heavy soils, clay.

Plants do die after a few years(6-10), or get very woody round the base and are better removed. However they usually leave seedlings behind that mature in a couple of years. I personally think that the species plants do better planted small in situ and allowed to grow undisturbed. Both foetidissimum and argutifolius reach flowering size in two seasons, going on to form domes about 3' across in garden soil, (they grow in cracks in rocks and near zero soil conditions in the wild).

Argutifolius plants bought already in flower may well be totally potbound and may suffer from having been grown in a very rich compost. When you plant them out the roots sometimes never escape from the original rootball into your own soil. Seem familiar??? Likewise I find that they struggle after division and never attain the shape and beauty of a seedling grown in situ.

See if you have some seed from the flowerheads and sow this where you want the plants, full sun, sharp drainage.

Hope this helps. Greenmanplants