SoftwareSerial ESP8266(REMOTEXY_SERIAL_RX, REMOTEXY_SERIAL_TX);   //init the serial protocol, define the RX and TX pins
....
ESP8266.begin(REMOTEXY_SERIAL_SPEED);

Why do you add these lines to the code?

Are you performing these functions  ?

SoftwareSerial ESP8266(REMOTEXY_SERIAL_RX, REMOTEXY_SERIAL_TX);   //init the serial protocol, define the RX and TX pins
....
ESP8266.begin(REMOTEXY_SERIAL_SPEED);

Why do you add these lines to the code?
http://remotexy.com/en/help/start/arduino-esp8266-ss/  see headline "If there is no connection ..."

//////////////////////////////////////////////
//        RemoteXY include library          //
//////////////////////////////////////////////

// RemoteXY select connection mode and include library 
#define REMOTEXY_MODE__ESP8266_SOFTSERIAL_POINT
#include <SoftwareSerial.h>
#include <RemoteXY.h>

// RemoteXY connection settings 
#define REMOTEXY_SERIAL_RX 2
#define REMOTEXY_SERIAL_TX 3
#define REMOTEXY_SERIAL_SPEED 9600
#define REMOTEXY_WIFI_SSID "Sky"
#define REMOTEXY_WIFI_PASSWORD "12345678"
#define REMOTEXY_SERVER_PORT 6377


// RemoteXY configurate  
#pragma pack(push, 1)
uint8_t RemoteXY_CONF[] =
  { 255,1,0,1,0,19,0,8,13,0,
  65,4,29,12,40,40,1,0,43,26,
  12,12,2,31,88,0 };
  
// this structure defines all the variables of your control interface 
struct {

    // input variable
  uint8_t button_1; // =1 if button pressed, else =0 

    // output variable
  uint8_t led_1_r; // =0..255 LED Red brightness 

    // other variable
  uint8_t connect_flag;  // =1 if wire connected, else =0 

} RemoteXY;
#pragma pack(pop)

/////////////////////////////////////////////
//           END RemoteXY include          //
/////////////////////////////////////////////

SoftwareSerial ESP8266(REMOTEXY_SERIAL_RX, REMOTEXY_SERIAL_TX);   //init the serial protocol, define the RX and TX pins




void setup() 
{
  RemoteXY_Init (); 
  
  ESP8266.begin(REMOTEXY_SERIAL_SPEED);
}

void loop() 
{ 
  RemoteXY_Handler ();
  
  RemoteXY.led_1_r = RemoteXY.button_1 * 255;
  delay(200);
}

I have used this before and it's SSID is "Sky"

My iPad is connected to the "Sky" WiFi network, but when RemoteXY tries to connect "New WiFi point device" I get "Error: (61) Connection refused"

Can anyone help me with this issue....