Hi VG. Wisley is an arching rose:
"The rose ‘Wisley’ bears magnificent large, cupped blooms that nod gracefully on a fine, arching shrub, so that in the mature plant they look directly at us. The flowers eventually open wide to form a more shallow cup and reveal numerous inner petals and a beautifully quartered centre. The colour is richest, pure deep pink; contrasting perfectly with rather shiny, rich green leaves. The fragrance is unusually fruity, with more than a hint of citrus, combined with the Old Rose scent." (David Austin website)
Your 'drooping' is the plant's natural arching :)