The US military has added more than 4,000 names to a federal background check database in the three months since a mass shooting revealed the organisation had consistently failed to report troubling convictions to the FBI.

Former Air Force member Devin Kelley killed 25 people, including a pregnant woman, in a mass shooting in Sutherland Springs, Texas in November. The gunman had received a bad conduct discharge from the Air Force in 2012 – a conviction that should have prevented him from ever buying a gun.

But the Air Force later admitted that it had not submitted Mr Kelley’s conviction to the FBI database used for background checks in gun purchases. The failure, the Air Force said in a statement, was “not an isolated incident”.

Three months later, the US military has added 4,284 names to the database – a 38 per cent increase, as first reported by CNN.

If the increase is a result of backlogged cases being added after the shooting, it suggests that thousands of people mistakenly maintained the ability to buy a gun for years.

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The number of dishonourable discharges in the FBI database has hovered around 11,000 since 2015, according to statistics published online. On 3 November, 2017 – two days before the shooting – the FBI had records of 11,313 dishonourable discharges, according to archived versions of the FBI website. By the end of January 2018, they had 15,597.

The US Marine Corps, Air Force and Navy all told CNN they had been reviewing old convictions for the database since the shooting. The Coast Guard said its numbers weren't included in the increase, and the Army declined to comment.

The Air Force announced in December that they would reform their reporting process and review 60,000 cases in which service members potentially should have been reported to the database. The Navy said that same month that it would review cases dating back to 1998.

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The FBI background check database helps gun sellers and law enforcement agencies distinguish legal buyers from those barred from having firearms. The military is required to report all dishonourable discharges to the database – meaning, all those convicted in military court of a crime equal to a felony. They must also report all bad conduct discharges for domestic violence or dealing drugs.

Mr Kelley pleaded guilty to assaulting his wife and stepson in 2012, and received a bad conduct discharge from the Air Force. But because this discharge was never reported, he was able to obtain the Ruger AR rifle he used in the shooting.

Similar issues with reporting are well-documented and widespread: The Defence Department Inspector General’s Office raised issues with reporting as early as 1997, and as recently as 2015. According to the Inspector General, the Air Force failed to submit records in approximately 14 per cent of its cases. The Navy did not submit records in approximately 36 per cent of cases, the Army in 41 per cent, and the Marine Corp in 36 per cent.

New York, Philadelphia, and San Francisco have all sued the Pentagon for failing to adequately maintain the database.

“It’s impossible to know how many instances of gun violence are tied to individuals who got guns but shouldn’t have,” Ken Taber, a lead attorney on the lawsuit, previously told The Independent.