Home Office data reveals that of the 8,391 residential burglaries recorded by the force in theÂ 12 months to March, 80 per cent of the cases -Â 6,709 - were loggedÂ as '˜investigation complete - no suspect identified'.
The figures also show that only half of the shoplifting casesÂ last year were solvedÂ -Â 5,477 out of 12,043.
Vehicle theft figures reveal that of the 2,773 cases recorded last year, 2,022 -Â 73 per cent -Â remain unsolved.Â
Nationally, police forces close investigations without identifying a suspect in three quarters of reported vehicle thefts, four in five residential burglaries and almost half of shoplifting cases.
The figures have prompted warnings that victims could be put off reporting offences, while criminals are given a -green light to re-offend'.
Police chiefs say increased demand and reduced officer numbers mean they have to prioritise cases where there is a realistic chance of prosecution.
MP Yvette Cooper, who chairs the Commons Home Affairs committee, said: "Too many investigations are closing without suspects being identified and we are hearing increasing reports of the police being too overstretched to investigate.
"Police forces are under immense pressure with rising serious and violent crime and changing patterns of crime alongside cuts in the numbers of officers and PCSOs.
"These figures suggest that investigations into volume crimes are now being hit. Failing to identify suspects gives criminals a green light to re-offend."
Alex Mayes, of Victim Support, said: "News like this could undermine confidence in the criminal justice system and prevent people reporting in the future."
Deputy Chief Constable Amanda Blakeman, the National Police Chiefs' Council lead for acquisitive crime, said increased demand and fewer officer numbers have led to forces prioritising cases with a realistic prospect of prosecution.
She added: "Police investigate all cases of theft, burglary and shoplifting. Particularly for these types of offences, police focus on targeting prolific offenders, organised crime networks, and ensuring prevention measures by homeowners and businesses are in place."
A Home Office spokesman said: "We expect the police to take all reports of crime seriously, to investigate and to bring the offenders to court so that they can receive appropriate punishment.
"However we recognise that crime is changing and police demand is becoming increasingly complex. That is why we have provided a strong and comprehensive Â£13 billion funding settlement to ensure the police have the resources they need to carry out their vital work.
"The Government remains alert to changes in trends and new methods used by criminals - and we will continue to work with the police, industry and others to consider the evidence and what more can be done to prevent these crimes taking place."
South Yorkshire Police has not yet commented.
But Dr Alan Billings, South Yorkshire's Police and Crime Commissioner, said: 'I recently attended a meeting of shopkeepers and small business owners in Crosspool where there had been a number of burglaries and the cases had been closed without a suspect being detected.
'Police officers who came with me explained that stretched resources means that incidents have to be triaged to determine which have the best chance of being detected and offenders prosecuted.
'While no one present liked the fact that this has to be done, all understood the reasons. The main plea from those attending was that they should be fully informed.'
He added: 'It is important that every incident is reported because this enables the police to see patterns of criminality -Â areas being targeted or similar methods of operation -Â and this may result in detections at a later stage.
'One of the shopkeepers also pointed out that we all have a responsibility to think about how we make our homes and businesses secure.
'I also visited this week the Crime Support Hub for South Yorkshire, based at Snig Hill, where a team of experienced detectives identify those cases which are most likely to result in a successful prosecution and they are having promising results.'