Management of the centre was transferred from private company G4S to the government's National Offender Manager Service (NOMS) in July last year, five months after claims of "unnecessary use of force and the use of improper language" were made in a BBC Panorama investigation into the establishment.
A report by Ofsted, following an inspection in June 2016, found that child protection matters were "not managed effectively" meaning young people "are not sufficiently safeguarded" and the establishment was rated "inadequate".
Following another visit conducted in March this year, the centre has been rated "inadequate" again, with concerns around the use of force, child safeguarding and the quality of staff being raised.
A joint inspection team made up of Care Quality Commission, Ofsted, and HM Inspectorate of Prisons found that, although the centre had made steady progress in a number of areas, it is still "inadequate" overall.
Problems with recruitment were noted, with the workforce having a number of vacancies. At the time of the inspection, only one recruit was enrolled on prison officer entry-level training.
Meanwhile, concerns were raised about levels of violence and the use of force. Although occupancy at the centre had been kept low since the last inspection, with fewer than 20 young people resident each month and falling to 11 young people in September 2016, use of force and restraint rose when the number of young people held increased.
In the four months before the inspection, force and restraint were used an average of 20 times a month.
"This average figure masks significant changes between months," the inspection report states.
"The increase in population immediately prior to the inspection led to a significant rise in incidents, which reached 40 in February 2017.
"This was a high figure given the population of young people living at the centre, which is relatively small despite the recent increase in numbers."
Inspectors did note that the behaviour of young people and staff appeared to have improved since the last inspection, with inspectors witnessing respectful, good humoured and useful discussions between staff and young people.
"Inspectors agree with senior managers that progress made so far is positive, but that there is more to do to fully embed good quality and consistent, secure childcare practice and management across the centre," the report states.
However, the report did raise concerns about security arrangements.
"There is a lack of understanding and knowledge at senior levels, leading to the potential for significant concerns to remain unaddressed," the report states.
"There have been several safety and security breaches that have impacted on the care of young people as well as the management of staff.
"For example, staff members have brought prohibited electronic items into secure areas. Inspectors were told that discussions were held with the staff involved, but there are no records of the actions taken to reduce the likelihood of reoccurrence."
Young people were also found to have been able to watch television channels containing "explicit sexual adult content".
"Senior managers have taken steps to address this and commissioned a permanent solution to avoid reoccurrence, but this is not yet in place."
The report adds that a number of initiatives are due to be implemented "soon" to address weaknesses identified in the inspection report.
"This includes the recruitment of restorative justice co-ordinators, restraint co-ordinators, and the creation of a wellbeing centre to rehouse a variety of health-related services," the report says.
"A centre-wide IT infrastructure should ensure that all staff can access up-to-date information about the young people they are caring for and be able to record incidents better.
"However, none of these measures are in place yet, resulting in some significant shortfalls outlined in this report."
Frances Crook, chief executive of the Howard League for Penal Reform, said: "Almost 18 months have passed since the BBC's shocking Panorama documentary, and yet today we read another awful report on Medway, which is clearly unfit to look after children.
"The G4S years were disastrous. Unfortunately, running Medway in the public sector does not appear to have made much difference. Children are still being placed in this jail, despite there being empty beds in the well run local authority units.
Carolyne Willow, director of children's rights charity Article 39, said: "Ministers must call time on the false optimism that this prison, and safeguarding mechanisms around it, can be made safe for children.
"Inspectors have rated the institution inadequate twice in a year and the local authority's response to safeguarding concerns continues to be deficient, with inspectors reporting a failure to follow statutory guidance.
"One quarter of children surveyed said they had felt unsafe there. This is intolerable from a child protection perspective and the prison must close."