STM32F4. Read data from UART. ERROR: Out of Memory!

I think I see the problem - you're setting a timeout to read back the data EVERY TIME you read from the serial port, so you end up with a crapload of timeouts. The number of reads you get before it dies at 9600 baud is (based on a quick estimate) consistent with storing the data (in a simple array, so it wastes tons of memory) AND creating a timeout for every byte. The solution is to only set the timeout once.

var LED_ORANGE = LED1;
var LED_GREEN  = LED2;
var LED_RED    = LED3;
var LED_BLUE   = LED4;
var arr=null;  
var timeout = null; //variable for timeout
function Toggle_Led(LED) {
 on = !on;
 digitalWrite(LED, on);
 return 1;
}
function Show(str) {
  console.log('**' + str);
}
function Thread1() {
  Toggle_Led(LED_ORANGE);
}
var Counter = 0;
Show("Start!");
// Тест UART
//==================================================================
Serial2.setup(9600, {rx:A3,tx:A2});
//USB.setup(9600, {dm:A11,dp:A12});
Serial2.on('data', function (data) {  // Receive function
  console.log(Counter + ") send");
  process.memory(); //This does nothing, other than possibly slow down code execution - did you mean to log it with console.log()? 
  if (data.length > 0) {  
    digitalWrite(LED_GREEN, 1);
    //console.log(data + "\n");
    
    if (arr == null)  {
      arr = new Array();
    }
    arr.push(data);          // Add new element
    // Таймаут приёма
    //==============================================================
    if (timeout == null) {  //If we haven't started the timeout yet, start it now, since we're getting data
        timeout=setTimeout(function (e) {
          console.log(process.memory());
          if (arr == null)  return;
          //for (var i=0; i<arr.length; i++)
          //{
          //  console.log(arr[i]);
          //}
          var str = arr.join("");
          console.log(str);
          
          arr = null;
          Serial2.println(str);        // Send
      
          digitalWrite(LED_GREEN, 0);
          digitalWrite(LED_RED, 0);
        }, 5000);
    } //Close the if...
    //==============================================================
  } else {
    digitalWrite(LED_RED, 1);
    console.log("Bad");
  }
  
  Counter++;
});
//==================================================================
setInterval(Thread1,3000);
Show("Stop!");
save();

For better memory usage, something like this would be a good start - by not creating the array and just building the string as it comes.

var LED_ORANGE = LED1;
var LED_GREEN  = LED2;
var LED_RED    = LED3;
var LED_BLUE   = LED4;
var str = ""; //no array, just a string.
var timeout = null; //variable for timeout
function Toggle_Led(LED) {
 on = !on;
 digitalWrite(LED, on);
 return 1;
}
function Show(str) {
  console.log('**' + str);
}
function Thread1() {
  Toggle_Led(LED_ORANGE);
}
var Counter = 0;
Show("Start!");
// Тест UART
//==================================================================
Serial2.setup(9600, {rx:A3,tx:A2});
//USB.setup(9600, {dm:A11,dp:A12});
Serial2.on('data', function (data) {  // Receive function
  console.log(Counter + ") send");
  process.memory();
  if (data.length > 0) {  
    digitalWrite(LED_GREEN, 1);
    str += data;
    //console.log(data + "\n");
    // Таймаут приёма
    //==============================================================
    if (timeout == null) {  //If we haven't started the timeout yet, start it now, since we're getting data
        timeout=setTimeout(function (e) {
          console.log(process.memory());
          if (str == "")  return;
          console.log(str);
          Serial2.println(str);        // Send
          digitalWrite(LED_GREEN, 0);
          digitalWrite(LED_RED, 0);
          timeout=null; //clear the timeout variable at the end
          str=""; //clear the string
        }, 5000);
    } 
    //==============================================================
  } else {
    digitalWrite(LED_RED, 1);
    console.log("Bad");
  }
  
  Counter++;
});
//==================================================================
setInterval(Thread1,3000);
Show("Stop!");
save();

Also, if you want it to work when running from flash, you might have to put the Serial2.on(...); inside an onInit() function. I don't recall whether Espruino will remember callbacks like that on save() or whether you need to set them in onInit().

(Note: My code is untested, might have typo/etc in it. Edit: just fixed one of them)

Edit: Even when it's "successful" in the case you've shown above, it looks like it's leaking oodles of memory....