The 55-year-old Informal Anarchist Federation (FAI) leader is having trouble walking and is using a wheelchair after losing more than 40kg on his strike against the 41 bis regime, the first Italian anarchist to be so treated.
Currently being held in Sassari Prison, Cospito fell in the shower and broke his nose two nights ago and lawyers and magistrates have sounded the alarm over his health, while his doctor has said he will be dead by April 20 unless he stops the strike.
There is an urgent need for Cospito to be transferred to a facility that can guarantee immediate medical care, the National Guarantor for Persons Deprived of their Liberty, Mauro Palma, said.
Palma has visited Cospito twice since he began his strike on October 20 and said on Thursday that his condition is "in progressive deterioration".
He added that "Sassari Prison (in northern Sardinia) is not fully equipped to treat him properly".
Cospito has been sliding ever deeper into poorer health because of his protest, his lawyer, Flavio Rossi Albertini, said on Thursday, after his fall the the previous night.
"All his (blood) values are falling and there is a risk of cerebral oedema", Rossi Albertini said.
A high court appeal hearing by Cospito on his prison treatment was set for April 20 on Wednesday, prompting his lawyer immediately file a plea to bring forward the high court hearing due to his concerning physical condition.
Cospito's doctor Angelica Milia said on Wednesday that if his current slide continues he will be dead "by April 20".
After his fall, she said that "he lost a lot of blood, he's weak, he's finding it hard to have a normal regulation of his body heat".
Amnesty International on Tuesday made a fresh appeal for Cospito, saying "we reiterate that it is the duty of the Italian authorities to fulfil their obligations to protect and respect the detainee's human rights, also taking into account the harsh conditions of the 41 bis regime to which he is subjected."
Cospito, who has been sentenced to four years of 41 bis while he is serving two sentences totalling 30 years for terror attacks, recently had an appeal turned down by a Rome surveillance court.
His lawyer said a fresh appeal to Justice Minister Carlo Nordio was "based on new information, not submitted to the Rome surveillance court".
As sit-ins and demos in favour of Cospito continue daily, judicial sources said the case would first have to go to Turin prosecutors again before Nordio can examine the plea.
There have been several recent FAI attacks in support of Cospito.
Judges recently ruled that Cospito should stay under the 41 bis conditions because otherwise there was a risk of his running FAI operations from inside jail.
On December 9 Greek anarchists linked to FAI claimed responsibility for the firebombing of two cars belonging to an Italian diplomat in the Greek capital a week previously.
The Greek group, which is named after a protester killed by a Carabiniere in self-defence at the 2001 Genoa G8 riots, said they were acting in solidarity with Cospito.
The group, Carlo Giuliani Vendetta Nucleus, said it was supporting the hunger strike of Cospito, who is serving 20 years for a bomb attack on a Carabinieri training academy at Fossano near Cuneo in Piedmont in 2006 and a further 10 years and eight months for wounding Ansaldo Nucleare managing diirector Roberto Adinolfi in Genoa in 2012.
The car bomb attacks against Athens embassy counsellor Susanna Schlein, sister of centre-left Democratic Party (PD) leadership candidate Elly Schlein, took place at dawn on Friday, December 2 and were soon attributed to anarchists like the FAI, who had shouted threatening slogans during Cospito's recent appeals trial.
Foreign Minister Antonio Tajani said Schlein survived the attacks "by a miracle".
Both Schlein sisters have now been assigned police protection.
After the firebombings, FAI militants issued the mocking message "Susanna Schlein should learn to park".
Rome prosecutors said last month they were opening a probe into arson attacks on ATMs and rubbish containers in two parts of the Italian capital on a recent Saturday night by Cospito supporters.
ANSA