Is there a statute of limitations preventing Jane from bringing this
case again, and if so can Jane request a restraining order for that
actions John had taken against her four years prior?
Based upon the title, I'm going to interpret this question more broadly and analyze if there is any legal doctrine that prevents Jane from bringing this case again.
Relevant Legal Doctrines
Double jeopardy applies to criminal cases where a trial has been commenced. A restraining order proceeding is not a criminal case, so this does not apply.
Res judicata and collateral estoppel are doctrines that prevent previously litigate issues from being retried, but they don't apply here because the case was not tried on the merits, it was apparently merely withdrawn voluntarily without being resolved (i.e. "dropped"). If the case were voluntarily "dismissed with prejudice" a new case based upon those events could not be tried again (but this doesn't seem to fit the facts).
Accord and satisfaction, and mutual release, are doctrines that apply when a formal settlement agreement is entered into that bars further litigation, but that doesn't appear to have happened in this case.
Statute of limitations bars many kinds of lawsuits, usually for money damages, from being filed within a certain amount of time after the incident occurred and the victim of the civil wrong learned of the wrong doing. The filing of the restraining order case establishes a date at which Jane definitely knew of the alleged wrongdoing. But, the statute of limitations varies greatly from jurisdiction to jurisdiction. In Colorado, the relevant statutes of limitations would be one and two years. But, this is not a uniform national rule since it is set by state law.
The typical statute of limitations for lawsuits alleging personal injuries in the U.S. ranges from two years to six year. It is longer than four years in Missouri (five years) and North Dakota (six years). Not infrequently, the statute of limitations for personal injuries caused by intentional acts is shorter than the statute of limitations for injuries caused by negligence.
There are also statutes of limitations for criminal cases, that run without regard to the knowledge of the alleged victim or the authorities in all cases that are relevant here. But, those vary wildly from state to state with some states having no strict statute of limitations for many criminal offenses. Generally speaking (subject to a handful of narrow exceptions) criminal cases must be brought by government prosecutors and can't be initiated by individuals alone.
Stale Incidents and Restraining Orders
Restraining orders are not barred by a statute of limitations because a restraining order assumes that there is a continuing and ongoing threat. Instead, the question is whether there is currently a threat from the person against whom the restraining order is sought to the person seeking the restraining order that is imminent.
Statements about four year old incidents, even if true, will rarely suffice on their own, to show that there is an imminent threat that makes the issuance of a restraining order necessary. But, evidence about incidents long ago (even decades old) can be relevant if this evidence, when considered together with evidence of more recent incidents, makes it appear that there is an imminent threat.
For example, suppose that someone actively threatened her ex-boyfriend with firearms, then was arrested and convicted of murdering someone else and spent fifteen years in prison, and then was released and starting making threatening phone calls to the same person. Even if an original restraining order cases was dropped by the ex-boyfriend after the arrest for murder because the problem was solved for the time being, the evidence of the pre-arrest conduct could be considered by a court to determine how seriously to evaluate the recent threatening phone calls.
Bottom line: It is unlikely that a new restraining order would be sought or granted based upon alleged four year old incidents, but the smart move would be to retain evidence showing that the four year old allegations were bogus in case these allegations are used as background facts in an alleged more recent incident.