The first step as an administrator is to find out why the payment was declined. Transaction Warehouse provides a report known as transaction diagnostics which gives you an idea why. Please view this topic for more information on this report.
An explanation of the difference between a swipe machine and online payment gateway:
A regular swipe machine is not picky about verification - the machine simply asks the CC company can we charge $xx to this card. If it comes back yes (and obviously not marked as stolen or expired) it approves it. It doesn't care about the address, security code, or other verification information.
The online gateway is a more modern and secure technology to protect against card theft as it checks in real time verification information such as address, zip code, and the security code on the back in addition to if the card has available credit to cover the purchase.
This would be why occasionally a card would be declined through the online payments, but if they call you or show up in person at your office it will work in your swipe machine.