Jatupat has been charged and remains in detention after sharing a BBC article deemed to be insulting to the monarchy last December. He was accused of violating the lese majeste and computer crime laws.
He was briefly released on bail, but his bail was revoked after investigators filed a complaint with the court alleging he had violated his bail condition.
His lawyers have filed several bail requests since then.
On Thursday, they made another attempt to allow Jatupat to appear for the exam outside the detention centre but failed, as the court rejected their request.