If you cannot find the tax invoice, and the purchase was more than $82.50, the GST cannot be claimed. You risk missing out on GST credit if you cannot find the tax invoice. This could mean hundreds of dollars in some cases. Remember: a credit card printout is not a valid tax invoice.
My recommendation is that you scan or photograph each tax invoice as you receive it. Send it directly to your Xero inbox to be attached to the transaction later when you reconcile your bank transactions. If you receive a tax invoice by email, simply forward the email to your Xero inbox.