Boonpattararakasa has been held since December after sharing a BBC news article on Facebook deemed to be unflattering to the country's new king.
Thailand has draconian lese majeste laws and viciously prosecutes slights to its royal leaders.
According to the Khaosod English news agency, after his fifth bail request was turned down in a secret hearing, Boonpattararakasa's father, Viboon Boonpattararaksa, said, "We will no longer appeal against his ongoing custody. We will not submit any more bail requests. Whatever they want to do, they're free to do it."
"This is what he arranged. He believes that it's no use," the elder Boonpattararakasa said.
His son was infuriated by the court's decision to decide his bail request in a secret hearing, without reporters or rights observers in attendance. He believes the procedure was illegitimate, his father continued.
According to Thailand's The Nation, the 25-year-old activist, also known as Pai Dao Din, was originally released on bail, but taken again into detention after a police officer in his hometown of Khon Kaen filed a petition saying Boonpattararaksa continued to incite on social media and could tamper with evidence if he remained free. He had been mocking the authorities over social media.
Boonpattararaksa is the only person to be arrested for sharing the particular article, despite thousands of others also posting it on social media sites. The student activist has taken part in anti-mining protests and campaigns to educate villagers about their land rights. He and others formed the New Democracy Movement (NDM) to call for democracy and elections in Thailand, which is ruled by a military government after the country's 12th successful coup since 1932, and has previously run afoul of the law for distributing pro-democracy leaflets and other activities.
Under the law, suspects can be remanded to custody for seven consecutive sessions lasting a total 84 days, according to Khaosod English. As Boonpattararaksa waits in jail, he is missing university exams and may be unable to graduate with his law degree as a result, his father said.
