She secured cross-party backing from Parliament for the measures earlier this year and said she was sending a clear message to judges that only in "exceptional circumstances" could they stop deportation moves on the grounds of a criminal's "right to family life". MPs of all parties voted unanimously in support of the stricter guidelines.
However in ruling that Mrs Olmazu could stay, a judge said the immigration courts still have significant leeway to decide whether deportations should take place.
In the gipsy fraud case, Lavinia Olmazu committed her crimes while employed as an "outreach worker" who was supposed to help gipsies and travellers integrate with British society.
Instead, she abused her position with two London councils and helped a gang produce forged documents which they sold to Romanian gipsies at £80 a time.
The false work documents enabled 172 Gipsies to obtain a National Insurance number and then claim work-related social security such as tax credits.
In all, £2.9 million was siphoned out of the public purse but detectives estimated the scam could have cost taxpayers up to £10 million if the authorities had not intervened when they did.
Olmazu was imprisoned for two years and three months.
But when the Home Office tried to deport her to Romania at the end of her sentence she persuaded immigration judges that it would breach her human rights because she has a 12 year-old son who she said was essentially British, having spent much of his life here. She claimed he did not speak Romanian fluently.
The Home Office appealed against the immigration court's decision but a senior judge ruled Olmazu's son had a right to continue his schooling in Britain.
The boy had been cared for by Olmazu's sister during her imprisonment and had been expected to leave the country on his mother's deportation. His father is a university lecturer in Romania.
Senior tribunal judge Andrew Jordan ruled that judges have considerable room for manoeuvre in deportation hearings, and said that different judges in lower courts - the "first tier tribunal" - will reach different decisions.
Judge Jordan said in his ruling: "There is inevitably room for different judges to reach a different conclusion on proportionality on the same facts.
"It is not the function of the Upper Tribunal to impose its view on proportionality unless the decision of the First Tier Tribunal is not legally sustainable."
He referred to a Court of Appeal ruling from six years ago in which Lord Justice Carnwath said that a judge's ruling did not necessarily have to be overturned if it appeared to be "unusually generous".
The Olmazu case opened in May, before the new rules came into force, but concluded in September after they took effect.
Olmazu now works for the Media Diversity Institute, a charity which has received hundreds of thousands in sponsorship from the Foreign Office and the Department for International Development.
Mrs Olmazu's case is not the only one in which judges have chosen not to follow Mrs May's view.
In another case a Chinese man jailed for a year in 2009 for possession of a false passport and fraud - and therefore due to be deported - was allowed to stay because he had married since his release.
The judge considering the case, Hugh Macleman, said that because Mrs May's rules did not spell out a "test" of what was an exceptional case, he could stay.
The Home Office last night came under renewed pressure to introduce clearer legislation to force judges to follow the Home Secretary's will.
Dominic Raab, the Conservative MP, said tougher action was needed to counter what he described as "judicial sabotage".
Mr Raab, a former government lawyer, said: "The Government targeted the right problem, but tinkering with the rules won't fix it.
"We need a new UK Borders Act that enables the authorities to remove serious criminals, ignore spurious human rights claims and override the current judicial sabotage."
