First, please review our PayPal Pro integration procedure to double-check that you haven't missed a step or overlooked anything:
http://www.e-junkie.com/ej/paypal-partner.htm
PayPal Pro checkouts using a credit card (when the buyer uses the Pay With Credit Card button in their cart) should be completed and processed almost instantly as soon as the buyer finishes checkout.
PayPal Pro checkouts going through PayPal's site (when the buyer uses the Checkout With PayPal button in their cart -- aka "PayPal Express Checkout" for PayPal Pro merchants) may be subject to delays between when a buyer finishes checkout vs. when PayPal finally completes the payment process and notifies our system of that payment, so our system can then process the order. Our system processes every sale the very instant we receive confirmation of completed payment from PayPal.
Your PayPal account should be set to approve all payments automatically, so they can complete the payment process and notify our system to process the sale ASAP. Even so, payments made through a buyer's PayPal account can still involve delays depending on what funding method the buyer selected for their payment, how quickly their bank responds, or just technical glitches or processing backlogs in PayPal's own system.