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Upon checking your form source code, I've found Jotform script reference which I think not used so I would suggest removing that.
Regarding on the problem, please re-embed your form using iframe. This is to prevent any possible conflicts that might make the file upload field to malfunction. http://www.jotform.me/help/148-Getting-the-Form-iFrame-Code
Here's a visual guide:
If your form users do continue to experience this problem, let us know here so we assist you further. Thanks!