After the reign of Ashoka it seems Hinduism continued strongly and would supplant both Buddhism and Jainism, why? Why did Hinduism remain dominant in India and why didn’t subsequently rulers adopt Buddhism also?
To clarify: Buddhism did continue on its ascendency for over a millennia after the time of Emperor Ashoka (~ 300 BCE). Buddhism was likely the dominant religious force in Northern India, more or less, till about the 6th century CE, while Southern India was a stronghold of Jainism. The Kushans, Indo-Greeks, Indo-Parthians, Sythians, and the Huns all tended to patronize Buddhism. It was only with the Guptas (mid third century CE) that a major empire favoured Brahmanical Orthodoxy. Even with the Guptas, it seems likely that the later emperors leaned towards Buddhism, while officially stating devotion to the family deity, Vishnu.
Even as late as the Emperor Harsha (~ 600 CE), Buddhism was widespread in Northern India, and the Chinese traveller Xuanzang attests to this. Harsha's own brother and sister were Buddhists, while his court poet notes Harsha as a devout Shaivite. Xuanzang records Harsha as Buddhist, and describes festivals where the emperor worshipped images of the Buddha. Xuanzang writes how Harsha would organise a charitable donation every five years, where he gave generously to holy men of all orders. Of the 21 days marked for charitable donations, four were for the Hindu holy men, while 16 were for the Buddhists. Does that suggest Harsha's leaning towards the Buddhists, or was this a consequence of the large number of Buddhist monks? Unclear.
What these and other sources indicate is that Buddhism was alive and well in Northern India, almost 1500 years after the time of Ashoka. We do know that shortly after the death of Harsha, Buddhism was in deep decline across India. The reasons are unclear. It was likely a combination of multiple factors, some of which include:
By the 11th century, Buddhism had practically disappeared from North India.