Someone else asked this a while ago. The answer is that there's no hard cap, and as long as you haven't set your security settings such that you hit your daily maximum, you should effectively be able to run any number of transactions. Authorize.net had 350,000 customers and processes 1/4 of US E-commerce transactions by dollar amount (according to their homepage), so I highly doubt your one server is capable of even coming close to overloading anything.
