Update limit in a stored procedure

I have a table with more then 20,000 records. this table has a record_id column. I want to change the record_id values based on a different sorting.
I wrote a stored procedure using a cursor running over all the records in that table (in the new order) and then for each record assign a new record_id.

when I run the stored procedure without the update, I get all 22,798 records. when I run it with the update I get only 4,838 records.
Is there a limit to the amount of record a stored procedure can update? can it be changed?

STORED PROCEDURE:
CREATE PROCEDURE sft_sort_table as
BEGIN
DECLARE @record_ID INT
DECLARE @MAX_record_ID INT
DECLARE @CUR_RECORD_ID INT

--Get the max rate_record_id
SELECT @MAX_record_ID INT = max(record_id) FROM table

DECLARE curRecord CURSOR FOR
select record_id from table order by new_sort
FOR UPDATE OF record_id
OPEN curRecord
FETCH NEXT FROM curRecord INTO @CUR_RECORD_ID
WHILE @@FETCH_STATUS = 0
BEGIN
SET @MAX_RECORD_ID = @MAX_RECORD_ID + 1
PRINT 'Record '
PRINT @CUR_RECORD_ID
Print 'will be '
PRINT @MAX_RECORD_ID
PRINT '-----------------------------'
--Update the record_id
UPDATE table SET record_id = @MAX_RECORD_ID
WHERE current of curRecord

FETCH NEXT FROM curRecord INTO @CUR_RECORD_ID
END
CLOSE curRecord;
DEALLOCATE curRecord;
END;

I'm questioning this line?

my assumption would be it should be like this

this is how I did it before, but it gives me the same results (only4838 records are update)