Yes, there is a limit to the number of email client tests you can perform per month, based on your subscription level:
Basic - 500 tests every 30 days
Professional - 500 tests every 30 days
Enterprise - 1,500 tests every 30 days
Each email client you select from the Preview in other boxes menu counts as one, individual test. You can see in the example below that four clients were tested last time, which means that four tests were performed towards the limit.