Does each I2C START signal need to be closed by a STOP signal?
Yes, this is called a "repeated start". Per the Wikipedia page:


  In a combined message, each read or write begins with a START and the slave address. After the first START in a combined message these are also called repeated START bits. Repeated START bits are not preceded by STOP bits, which is how slaves know the next transfer is part of the same message.


In a multi-master configuration, a repeated start also ensures that another master can't grab the bus between two different transactions.