Poi has no built in sorting mechanism, though of course you are far from the first one with that need.
I think you are getting in trouble because you are moving rows that you are iterating over. I have run the code above and it seems what is happening is rows are disappearing from the sheet by the end of the code execution.
The question attempts to do an in-place modification of a read-in sheet. I believe that creating a second output sheet would be more appropriate.
So the basic approach would be read the sheet, sort in java just as you would treat any other sort problem, write to output sheet. If you did a map of the row number which is unique to the string value of the column you are interested in then you could sort the map by value. This sort of approach would work if you only foresaw the need to sort on a single column. In any event, it is not as simple as just choosing the sort menu option from within excel.