Is it possiable for the prosecution to run out of time in the case against you?

If you haven't yet been arrested there is a time limit the prosecution has to file charges against you for most crimes except for murder. This is called a statute of limitation. The law varies from state to state and crime to crime. For specific information you will have to look up the statute for the crime you are suspected of and the jurisdiction of the alleged crime. The limit can also vary in the time that it starts from the date of the crime to the first time it was reported.

If you've already been arrested you are guaranteed the right not to be held without charge and your arrest being reviewed by a judge. This is normally 24-48 hours, but this can vary depending on where on if its a deadline or a guideline.

After this you have to be indicted by a grand jury. You probably won't be invited. The Federal limit for indictments after arrest is 30 days. This also varies by jurisdiction.

After this you have the right to a "speedy" trial. Guess what? this is also depending on where you are! Some places require you to demand a speedy trial in writing and start the psuedo clock then. Some have guidelines in place but you must make a motion to the court about how your trial isn't speedy enough and the court will decide how speedy is "reasonable"

Then, if they ever do let you go. They can always arrest you again for the same crime and try all over again until the statute of limitations is up.

In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defense."

And if your declared an "Enemy Combatant" forget it, they can hold you for how ever long they want because all they have to do is say the 'T' word.