Sometimes banks will fail a Credit Card and give you the error of "Security code is invalid". Most of the time this is due to one of 2 things;
A typo. Yes, it can be as simple as that. Incorrect entry of card number or CVC code.
The customer may have been sent a new card. Sometimes banks will issue a new card with the same card number but a new updated CVC number. They could be trying to enter the old combo without realizing.
If this happens to you often and you are sure your CVC codes are correct you can turn off this check in stripes settings.
Login to your Stripe dashboard at www.stripe.com (if you do not know your password, you can reset it).
On the upper right of the screen, click on your name and then on "Account Settings"
On the bottom of the first tab (General), make sure "Charges that fail CVC verification" and "Charges that fail zip code verification" are both unchecked.