nvarchar(max) holds one or two gb. It's not the problem. There are a number of possible issues here, the most likely is that you are using other variables in the construction of the string, and they are not all nvarchar(max). Can you post a little more detail? Some code?
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden