There are a number of causes that can result in your customers' credit card charges not being successful. Some of these causes start with your customer, or with their bank, or with your payment gateway/merchant account, or with your payment gateway settings in Chargify.
Here's a brief summary of areas where a failure can occur:
Your customer's credit card may be expired or over its limit, or your customer may have given the wrong billing address or zip code, or there may be a fraud alert on their card for some reason.
Always try more than one credit card (like some of your own) so you can narrow down where the problem is really located.
If only one customer is having problems, then you know the problem lies with their card OR SOMETHING ABOUT THEM. For instance, if you are in the USA and they are in Australia, maybe their credit card bank is blocking because they think it's strange/unusual, or maybe your payment gateway is blocking (see below).
Blocking by Payment Gateway
Your payment gateway, such as Authorize.net, has many settings that allow or block transactions in different circumstances.
For instance, your gateway account has settings that tell them how to react if there is a billing address mismatch with your customer's credit card, or if the customer's card-issuing bank does not support address verification, or if their card bank is outside the USA, or if the card bank is simply in a different country than the merchant (you), etc.
These settings inside your gateway account are meant to protect you from fraudulent charges. You will need to log into your payment gateway website and adjust these settings as you learn your customer profile and behavior.
You may need to "loosen" the settings to let more customers in, but keep in mind that the more you loosen these settings, the easier it will be for someone to do a fraudulent transaction. It's a balance between making it easy for your customers, yet stopping fraudulent transactions.
Payment Gateway Misconfiguration in Chargify
Your payment gateway may be working fine itself, but the username & password that you configured in Chargify may be incorrect. See the links below for more detailed documents on this.
Blocking by Merchant Account
This is less common, but your merchant account may be denying the transaction or may not be set up to accept the transaction. For example, your merchant account may impose a total monthly charge limit if you are a new business or your merchant account is new. Or if you did not specifically request it, most merchant accounts are not set up to process American Express charges, even if your payment gateway is okay with AmEx.
See this Gateway Troubleshooting Guide for ideas you can test.
See this Blog Entry for a detailed explanation of payment gateways and merchant accounts.