We have had a few customers who get a Paypal Access Denied error when trying to checkout with Paypal. The error is on the PayPal site. We have talked to Paypal Merchant Support on the phone. They tell us it is definitely happening on the PayPal site and is some kind of new blocking algorithm from Paypal Security and that the customer will have to call them directly at 1-888-221-1161.
There are also several people talking about this issue in the Paypal Community Forum. We saw a couple of possible solutions there.
"Try clearing your browser cache and cookies and restart device."
"Try rebooting your modem in order to get a new IP Address from your internet service."