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In the 7th book, when Ron is eventually able to tune in to the Potterwatch radio station with the password "Albus", they mention that there was an attempt to arrest Hagrid for hosting an event at Hogwarts in support of Harry. This means that he remained at Hogwarts for a number of months into Harry's would-be 7th year.

Why was Hagrid allowed to remain at Hogwarts for so long, seeing as he is half giant, associated with the Order of the Phoenix, and a known close friend of Harry's?

Any of these things alone would be possible reasons for Snape, under Voldemort's orders, to expel him from the school, or otherwise attempt to arrest or even attack him.

My only guess is they had hoped Harry might attempt to return to Hogwarts to visit Hagrid? Is there anything in the book mentioned that might give a solid hint about the reasoning behind this?

I can think of a few possible reasons.

1. Voldemort's regime was predicated on projecting a sense of normalcy despite his secretly controlling things behind the scenes. Hagrid's treatment is not that different than the treatment received by the Weasleys, who were allowed to continue to live normal lives while under constant surveillance. It's only once Ron was outed as traveling with Harry that they were forced to flee, despite their obvious sympathies from the start. McGonnagal, another former member of the Order of the Phoenix, is also allowed to continue to teach.




2. This was likely Snape's doing. Elsewhere in Deathly Hallows it's mentioned that Snape has placed Hagrid in charge of "punishing" students by making them work in the Forbidden Forest. While certainly frightening, in reality it was far safer and less traumatic than being tortured by the Carrows. Snape faced the difficult task of publicly appearing to support Voldemort's regime while protecting the students and staff, so presumably he came up with a reason to protect Hagrid until the situation became untenable.




3. The Ministry previously attempted to arrest Hagrid in Order of the Phoenix. It ended with the Aurors getting their butts kicked and Hagrid running into the forest. His giant blood grants him a degree of immunity to curses and spells that makes him an incredibly dangerous opponent. Why not let sleeping dragons lie?




4. Conversely, a frequent theme of the books is the Death Eaters' arrogance and failure to understand the strength of those who are "beneath" them. In their eyes, Hagrid is an uneducated, feral halfbreed without a wand. They don't even kill Hagrid during the Battle of Hogwarts, only tying him up to mock him.