I do not practice in NC, but I can offer some general advice.  Assuming this is a criminal case, it can be continued for as long as necessary and as long as the judge allows continuances.  There are many reasons to continue a case: more discovery, locating witnesses, allowing a defendant to get treatment, etc. 

I do not practice in North Carolina but the general rule throughout the country is that whether to grant a continuance is within the discretion of the trial judge.  If you are a defendant in a criminal case you may move for speedy trial but there may be adverse consequences.  In Florida, in a civil case, persons over a certain age have a statutory right to request their case be a priority on the judge's trial docket. 

Is this a criminal case involving a violation of a 50B?  The number of continuances varies by county and judge.  In Wake County, where I practice criminal law, each side might get 3 continuances in a misdemeanor case (not involving DWI) at which point the file is marked "last".  However, a judge can continue the case beyond 3 or even 4, especially if one side shows good cause. 

Note, there is no speedy trial statute in North Carolina.  So your speedy trial remedies in criminal law are extremely limited, and not really applicable unless we're talking about very long periods of delay that would implicate the Federal Constitution.  Think years, not months.