I'm not aware of any limitation on adjournments by the court, but if it is a criminal case, the Speedy Trial Act applies, and you should ask your lawyer about this.
If it's a civil case, it depends on the reasons why the case has been adjourned repeatedly. If they've all been at the other side's request, you should get a lawyer immediately. If the other side has a lawyer and you don't, you're at a distinct disadvantage. If you have a lawyer and s/he can't explain to you what's happening and what can be done about it.
Very often, cases are adjourned for particular reasons that are entirely legitimate, although to a layman they can seem excessive. If you can't get satisfactory answers from your attorney, or you don't have one, consult another attorney.
DISCLAIMER - THIS IS NOT LEGAL ADVICE. THIS IS FOR GENERAL INFORMATIONAL PURPOSES ONLY, AND DOES NOT APPLY TO ANY PARTICULAR PERSON OR CASE. NO ATTORNEY-CLIENT RELATIONSHIP IS HEREBY CREATED.
For civil matters in Virginia, it depends on the court. Many cases get continued because parties are unavailable, because witnesses are unavailable, because the judge is unavailable, because tests have not been completed, or because the parties are trying to settle.
If you have an attorney, contact your attorney for a reason. If not, contact the court and ask; the file will have the reason. You can find the courts information at www.courts.state.va.us
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]
To build on what the previous answers have provided, it is not clear from your question whether the new trial dates are ordered by the judge, or at the request of opposing party.
If by the judge, there is (by definition) no limit, because the judge is the one that controls the courtroom. Sometimes there are just too many cases to be heard in that courtroom on that day ... similar to an airplane overbooking the flight. Sometimes the judge reschedules the case to "force" the parties to keep talking settlement. The reasons are only limited by the imagination of the judge, since there is no one (other than the presiding judge) and nothing (other than the Canons of Judicial Performance) to require the judge to hear a particular a particular case at a particular time.
On the other hand, if the case is continued at the request of opposing party, each request must show "good cause" for the new date. "Good cause" is a loosely defined reason, and is is entirely up the judge, in his/her discretion, to determine whether the reason/excuse for the request for a new date is good enough.
One limitation, though, your state certainly has a statute that forces mandatory dismissal of the case if it is not brought to trial within a certain period of time. In California, that limit is five years from the date the complaint is filed. So, be certain that the judge does not give a new trial date *beyond* your state's statutory maximum time.
This is general information, since I"m not licensed to practice in Virginia. Of course, this does not mean we have an attorney-client relationship.