According to the source code:

<!-- language-all: lang-cpp -->

    const static unsigned int max_frame_payload_size = MAX_FRAME_SIZE-sizeof(RF24NetworkHeader);

that would be `24 bytes`. Maximum lenght of payload for NRF24L01+ is 32 bytes and the `RF24NetworkHeader` seem to be 8 bytes long. So you can send up to 24 bytes in one package.

**EDIT:**  
Here is the stripped `RF24NetworkHeader` declaration code from which can be seen `sizeof(RF24NetworkHeader)` is 8 bytes.

    struct RF24NetworkHeader {
      uint16_t from_node;			// 2 bytes
      uint16_t to_node;				// 2 bytes
      uint16_t id;					// 2 bytes
      unsigned char type;			// 1 byte
      unsigned char reserved;		// 1 byte
      static uint16_t next_id;		// static member doesn't count for sizeof()
      RF24NetworkHeader() {}
      RF24NetworkHeader(uint16_t _to, unsigned char _type = 0): to_node(_to), id(next_id++), type(_type) {}
      const char* toString(void) const;
    };