Siddham stopped being written in India. The hands descended from Gupta Brahmi continued to develop there and became the scripts of the north, and the particular form that had been carried east was superseded at home like any other stage of a living tradition. Nothing was lost from the Indian point of view, because what replaced it did the same job.
It survived because it had been taken somewhere it could not be replaced. In China and then in Japan the script was needed for one purpose, writing Sanskrit syllables that were not to be translated, and no local script could do that job, so there was never a successor for it to be superseded by. Shingon and Tendai kept it in liturgical use, the shittan scholars kept it as a subject, the stonemasons and woodcarvers kept it in the open air, and the printers multiplied it.
The result is a script preserved by a tradition that did not speak its language, for a purpose the language itself had not been shaped for, in a country a long way from where it was made. It is now written by calligraphers, cut on grave markers, printed on charms, taught in temples, studied by philologists and encoded for computers, and the forty-seven letters are the same forty-seven the Sanskrit phoneticians set out, in the same order, describing the same mouth.