They don’t seem that interested in hot pursuit. It took private sleuths hired by Medicare an average of six months last year to refer fraud cases to law enforcement. According to congressional investigators, the exact average was 178 days. In that time frame, many cases can go cold, making it difficult to catch perpetrators, much less recover money for taxpayers. A recent inspector general report also raised questions about the contractors, who play an important role in Medicare’s overall effort to combat fraud. Out of $835 million in questionable Medicare payments identified by private contractors in 2007, the government was able to recover only about $55 million, or about 7 percent, the report found. Medicare overpayments — anything from a billing error to a flagrant scam — totaled more than $36 billion in 2009, according to the Obama administration.