IMPORTANT: This issue has now been resolved via an official hotfix from Microsoft. Please see Error message when you try to attach a file in a custom form on the Web site in Windows SharePoint Services 3.0: “This form was customized not working with attachment”.
As posted by Marc Davis, there is an unsupported workaround for retaining attachment functionality with your custom list forms. For some time now, we’ve been supplying the workaround free of cost to customers who’ve opened support cases and requested a fix. We are okay with the Marc’s posting, and to be honest something like this was bound to happen, considering our delay in posting the MSDN documentation for the issue. I am also relieved to see Marc’s disclaimer in bold red. We understand your guys’ frustration with the attachment problem, and I apologize we didn’t post the workaround earlier. We just don’t generally like providing unsupported cumbersome workarounds. Although I can’t guarantee or give anything “official,” I can hint that you may be seeing a real fix circa SP2 time frame. May be a ray of light at the end of the tunnel, yet.