With the exception of murder, there is always a time limit. That time limit depends on a number of facts besides when the case actually goes to trial. For example, did you waive time? Have you ever withdrawn that waiver? See your attorney.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
There is a three year statutes of limitations for the charging of the OWI and the charging tolls the statute of limitations (not for the trial)
In accordance with the Avvo community guidelines, this communication does not constitute "legal advice", nor does it form an attorney-client relationship. You should seek counsel in your geographic area regarding any specific questions.
Statutes of limitation go to the time limits for commencing a prosecution, so if you have had an open case since 2011, it simply does not apply to your situation. While the age of the case is unusual, it is not, by itself, grounds for dismissal. If your contested case has been open this long, I suspect you may have a lawyer. If so, that person, who is familiar with your case, is in a far better position to answer questions than anyone on the web. Schedule a time to review your concerns with your lawyer. If you don't have one, get one. Good luck.
This answer is provided for general information only. No legal advice can be given without a consult as to the specifics of the case.