N.H. Rev. Stat. Ann. § 282-A:49

If no appeal from a determination by a certifying officer is taken within the time limits in RSA 282-A:48, such determination shall thereupon become final and benefits shall be paid or denied in accordance therewith, subject to the provision in RSA 282-A:48 relative to good cause for late filing of the appeal; provided, however, that the certifying officer's determination shall continue to have effect as though no appeal had been filed with respect to all weeks of unemployment and any amount not affected by the appeal.