This is unfortunately an all-too-common issue facing Visa cardholders. Acceptance rates vary between about 60% and 80% depending on the specific poker site you're trying to deposit to and the particular issuer of your card. In some cases, your transaction will be flagged because it's out-of-line with the usual purchases you make, and a simple call to your financial institution's cardholder services team will clear everything up. Don't tell them that you're using your Visa card at an online poker site – simply inform them that you're making a purchase from an online merchant.
If your deposit still won't go through, call up the poker company yourself and explain the situation. These firms have a lot of experience helping clients who encounter problems when attempting to deposit money. They might even be able to open up special deposit methods for you that they don't offer in their standard menu of options.