Don't do that. Never concatenate strings to build a SQL command. It leaves you wide open to accidental or deliberate SQL Injection attack which can destroy your entire database. Always use Parameterized queries instead.
When you concatenate strings, you cause problems because SQL receives commands like:
SELECT * FROM MyTable WHERE StreetAddress = 'Baker's Wood'
The quote the user added terminates the string as far as SQL is concerned and you get problems. But it could be worse. If I come along and type this instead: "x';DROP TABLE MyTable;--" Then SQL receives a very different command:
SELECT * FROM MyTable WHERE StreetAddress = 'x';DROP TABLE MyTable;
Which SQL sees as three separate commands:
SELECT * FROM MyTable WHERE StreetAddress = 'x';
A perfectly valid SELECT
DROP TABLE MyTable;
A perfectly valid "delete the table" command
And everything else is a comment.
So it does: selects any matching rows, deletes the table from the DB, and ignores anything else.
So ALWAYS use parameterized queries! Or be prepared to restore your DB from backup frequently. You do take backups regularly, don't you?
While your code fragment doesn't directly expose you to SQL Injection, it does expose you to other problems - like the DB server not using the same default date format as your application, at which point you start to get intermittent problems: app crashes, invalid data, you know the kind of thing.
Pass the dates as DateTime directly as parameters instead of converting them to strings, and those problems disappear.
BTW: You can also use SQL BETWEEN to compare:
... WHILE @DateToCompare BETWEEN Date1 AND Date2
But check the rest of your app and replace any concatenation with parameters!