If the case was dropped prior to the matter going to trial, it is possible for the prosecution to file charges again later.
They can do this based on new evidence, or different policies, or perhaps even a change in prosecutor's office, or charges being sought (for example, if the original complaint was contemplated by the local DA, and they decided not to prosecute, but the US Attorney General decided to pursue federal charges in federal court).
If the matter is dismissed prior to trial, the defendant's right against "double jeopardy" is not invoked as they were never tried in the initial matter. So it is possible to be tried again.
The defendant is entitled to all defenses that may apply, including the statute of limitations (the statute is not tolled during the original charging period, it "accrues" - starts - at the time of the original action, and continues until it runs out, or the charges are actually filed).
As with any criminal action, if you are facing criminal prosecution, do not speak with law enforcement or prosecutors without your lawyer present. Even "informal" discussions can lead to incriminating statements. If you cannot afford an attorney, ask that a lawyer be appointed to represent you. You cannot be compelled to speak with law enforcement without a lawyer present.