When processes on two different machines communicate, they most often do so using the TCP protocol. While TCP is appropriate for a wide range of applications, it has shortcomings in other application areas. One of these areas is fault tolerant distributed computing. For some of those applications, TCP does not address link failures adequately: TCP breaks the connection if connectivity is lost for some duration (typically minutes). This is sometimes undesirable. The paper proposes robust TCP connections, a solution to the problem of broken TCP connections. The paper presents a session layer protocol on top of TCP that ensures reconnection, and provides exactly-once delivery for all transmitted data. A prototype has been implemented as a Java library. The prototype has less than 10% overhead on TCP sockets with respect to the most important performance figures.