In a leaked letter, Mr Skates said he was informed this was because of the current level of investment.
He meets Network Rail officials on Thursday after describing conditions for rail passengers as "unacceptable".
Network Rail said it was committed to working with the Welsh Government to get value for taxpayers' money.
Mr Skates has accused the company - which maintains tracks across the UK - of a lack of investment in clearing leaves this autumn, which cause damage to train wheels because of the extra braking pressure required.
He believes this has led to over-crowding and reduced punctuality of services as it forces more rolling stock to be removed from routes.
Arriva Trains Wales said 54 out of its fleet of 127 have had to be taken away for repairs this autumn - an increase of 54% on the same period last year.
In the letter seen by BBC Wales, sent last month to Network Rail's route managing director Andy Thomas, Mr Skates said Arriva Trains Wales raised concerns about the level of work being carried out to clear leaves from the lines.
He wrote: "I have been informed that Network Rail responded that this was due to budgetary reasons and that at the current level of investment it would take 28 years to get the Welsh network up to the prescribed standard."
A Network Rail spokesman said: "We have jointly concluded with Arriva Trains Wales that the reduction in fleet availability cannot be solely related to Network Rail's autumn plan as we are increasing spend and activity.
"We are committed to working jointly with Arriva Trains Wales and the Welsh Government to ensure maximum value for taxpayers' money."
In a debate at the Senedd on Wednesday, Plaid Cymru's economy spokesman Adam Price described current conditions for Welsh rail passengers as a "national crisis".
He referred to three examples on social media yesterday in which one passenger told of his experience of a train catching fire, one had been on an overcrowded service where a passenger fainted, and another claimed to have a seat for the first time in 11 months.
An Arriva Trains Wales spokesman denied one of its trains had caught fire, instead saying there was a problem with an exhaust.
He said: "We understand and apologise for the frustrations around the capacity issues faced by commuters which has been made worse recently by the additional maintenance required on damaged train wheels caused by the autumn leaf-fall.
"We continue to work hard with our partners in Network Rail to reduce the impact of this issue."

Thomas Fendall and Jessica Hussell, who were in a relationship, used their positions within Greater Manchester Police to access restricted material.
A court heard they targeted Hussell's ex-boyfriend, who lost his job after he was wrongfully arrested.
Fendall was jailed for 19 months and Hussell was sentenced to 16 months.
The pair provided false information to the charity Crimestoppers, naming Hussell's former boyfriend as being responsible for a fail-to-stop collision in which another PCSO was injured.
Brett Gerrity, senior crown prosecutor for CPS North West, said: "Thomas Fendall and Jessica Hussell, who were in a personal relationship, abused their positions within the police to access restricted material on the police computer system for their own use and to settle a personal grievance.
"Fendall used the police computer system to research background information on people he and Hussell knew, and shared information and documents with others.
"They provided Crimestoppers with bogus information leading to an innocent man being investigated by the police for attempted murder."
He continued: "They also supplied the DVLA with fictitious intelligence, which led to the same man having his driving licence revoked.
"He had to prove he was medically fit to drive before his licence could be reinstated two months later."
Sergeant Lee Westhead, of GMP's Serious Collision Investigation Unit, said: "The actions of Fendall and Hussell undermine everything that is at the heart of policing in this country."
Hussell, 19, from Glossop, and Fendall, 26, from Denton, each pleaded guilty to misconduct in a public office.
They also pleaded guilty to perverting the course of justice in relation to providing false information to Crimestoppers.
Fendall had pleaded guilty to another count of misconduct in a public office and four counts of computer misuse relating to the GMP intelligence system.
The pair were arrested in August 2015 after an investigation by GMP's Serious Collision investigation Unit. They were suspended from GMP upon arrest.
Network Rail believes it will take 28 years to get the Welsh rail system up to standard, Economy Secretary Ken Skates has been told.
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Two police community support officers have been jailed for using force computers to try to frame an innocent man for attempted murder.