Aside from the TWS API's inherent limitation of 50 messages per second implying a maximum of 50 orders per second being sent to the TWS, there are no further API-only limitations. Interactive Brokers however requires its users to monitor their Order Efficiency Ratio (OER) as detailed in the Considerations for Optimizing Order Efficiency IBKB article.

Additionally, please note IB allows up to 20 active orders per contract per side per account.