Most secret service details are protection for heads of government/state and thus their details would be afforded Sovereign Immunity (Such as POTUS, VPOTUS, and First and Second Families) OR Diplomatic Immunity (visiting dignitaries and leaders of other nations). Typically there are more diplomatic ways to handle the cases in the latter.
In the former case, thus far, it has not been handled. During visits, the traditional Executives and Families are usually closely guarded by the Service with additional law enforcement form local jurisdictions called in to aid in the protection, usually to secure routes the Motorcade will take to a designation (I speak from personal experience, POTUS coming to town is a nightmare on traffic). If they are speeding, they are typically doing so down a completely empty highway with police escort.
From this point, most under of the Service would be monitored and controlled so closely, at least one Agent would notice if any protected was committing a crime and would have to write it up in a report. There is also considerable debate in legal circles if the President and Vice President could be arrested for a crime while in office, with the general acceptance being that they could not and would need to be impeached by congress. Secret Service will continue to protect former Presidents and Vice Presidents for life, along with their spouses and children up to a certain age.
With all that in mind, it would not so much be that the Secret Service would prevent arrest of an individual under their protection so much as the Secret Service would be the arresting authority. As they are law enforcement agents under the Federal Government, they can legally arrest people and then hand them to the proper law enforcement agency to effect the arrest. This would mostly happen with candidates for office OR former presidents OR family at any point in time as the scenario described is a bit harder to make a legitimate arrest.
In fact, the Secret Service does have arrest authority with one of the highest conviction rates of any Law Enforcement Agency in the Country. It's just most crimes they arrest have nothing to do with threats to those under their protection. The Secret Service is also charged with investigation of counterfeiting of US currency and they are very good at it. This was actually their original sole function in the U.S. government and they still exist under the Treasury Department to this day. At this point, if you're wondering how they got the job of protecting important people in the executive branch from that, well, it's simple. At the time of his assasination, the legislation to create the USSS was on Licoln's desk. At the time of their creation, the only other Federal Police services were the U.S. Park Police, the Postal Inspection Service, and the U.S. Marshals. The first two had specific jurisdictions and the Marshals were undermanned so the USSS was tasked with investigating all sorts of financial crimes and quickly became the most successful U.S. Law Enforcement Service. They were also the first U.S. Intelligence and Counterintelligence agency (though they no longer are part of the Intelligence Community) until the FBI took on those duties. So following the Assassination of William McKinley in 1901, Congress authorized them to take up full time Presidential Protection because at the time, they were pretty much doing everything else.