It happens. People get arrested for DUI and other criminal offenses every day. Many face the fear they'll lose their jobs over it. If their jobs are public enough, sometimes they even feel pressure to resign though they have a great criminal defense attorney, have every intention of fighting for themselves, and might actually not be guilty of the charges they face.
Consider the sad tale of one J. Randolph Babbitt. Yes, that Babbitt, the former head of the Federal Aviation Administration, who resigned in shame over his DUI arrest amid public outcry. UPI reports today that Mr. Babbitt's DUI was recently dismissed due a violation of Babbitt's Constitutional rights protecting him (and you) from unlawful arrest. The police must have probable cause to make an arrest for DUI, and in this case, the Judge did not see it.
Meanwhile, Mr. Babbitt is out of a job.