Why is this not deterministic?

I'm using SQL 2008 (not R2). When I try to define the following UDF and try to use it in a computed column, I get the ever popular "cannot be persisted because the column is non-deterministic".

set ansi_nulls on
go
set quoted_identifiers on
go
create function [dbo].[RemoveNonAlphanumeric]
( @input nvarchar(100)
)
returns nvarchar(100)
AS
BEGIN
    declare @i int, @result nvarchar(100), @pattern nvarchar(100);
    set @pattern = '%[^a-zA-Z0-9]%';
    set @result = @input;
    set @i = patindex( @pattern, @result);
    while @i > 0
    begin
        set @result = STUFF( @result, @i, 1, '' );
        set @i = patindex( @pattern, @result );
    end
    return @result;
END

using SELECT OBJECTPROPERTYEX( object_id('dbo.RemoveNonAlphanumeric'), 'IsDeterministic' ) gives back zero. I've tried changing both ansi_nulls and quoted_identifier to OFF with no effect on the determinism of the function.

I've even replaced the body of the UDF with a simple return N''; and SQL Server STILL says it is non-deterministic.

I am simply not seeing what is non-deterministic. Any help would be apprectiated.