on change

I don't see an obvious issue. It may be a caching issue on either the browser side or server side. Since we're showing possible code improvements, I would do the following:

<cfparam name="form.code" default="" />

<cfoutput>

<form action="#cgi.SCRIPT_NAME#" method="post" name="mycode">
<select name="code" required="yes" onchange="this.form.submit()">
<option value=""><b>Select Customer</b></option>
<option value="AB" <cfif form.code eq "AB">selected</cfif>>AB- None</option>
<option value="CD" <cfif form.code eq "CD">selected</cfif>>CD- Deliver</option>
</select>
</form>

#code#
</cfoutput>

I would also add jquery validation to require a selction by the user (assuming that it is a required field). But all the is off topic.

It should work. In any case, you could improve slightly on the logic like this

<cfform name="mycode">

    <select name="code" required="yes" onchange="this.form.submit()">

        <option value="">Select Customer</option>

        <cfif isDefined('form.code')>

        <option value="AB" <cfif form.code eq "AB">selected</cfif>>AB- None</option>

        <option value="CD" <cfif form.code eq "CD">selected</cfif>>CD- Deliver</option>

        <cfelse>

        <option value="AB">AB- None</option>

        <option value="CD">CD- Deliver</option>

        </cfif>

    </select>

</cfform>

<cfif isDefined('form.code')>

    <cfoutput>#form.code#</cfoutput>

</cfif>