At a few minutes past 10 a.m. on Monday, as the Supreme Court began to issue the final rulings of the term, 60,000 people — including journalists at major news outlets around the country — were following the live feed of Scotusblog, a website devoted to covering every warp and woof of the court’s complex litigation. Since its inception in 2002, the site has become required reading for Supreme Court news and analysis, winning multiple awards.

Yet Scotusblog’s ability to cover the court remains precarious because it has repeatedly been denied a press credential. (The site has gotten around this for now because Lyle Denniston, its lead reporter and a five-decade veteran of Supreme Court reporting, is separately credentialed through a radio station.)

What’s the problem? The Supreme Court has traditionally recognized credentials issued by the Senate’s Standing Committee of Correspondents, which is made up of journalists from mainstream news organizations. In April, the committee denied Scotusblog’s latest request for a credential because its founder and publisher, Tom Goldstein, is a lawyer whose firm argues regularly before the court. The committee said that that violates its rule against lobbying the federal government. It also said the site is not independent from Mr. Goldstein’s firm.

These arguments are tenuous at best. Litigating is not lobbying, but, even so, the committee has credentialed, among others, foreign journalists from state-run publications whose countries routinely lobby. And Mr. Goldstein has erected firewalls to assure that the firm’s work does not editorially influence the blog.