STM32 UART Transmit stops responding after some time

Use code formatting as it makes it easier to read code

You say "And have stopped and restarted my HAL_UART_Receive_IT()" but I don't see it in your code you've posted. So if HAL returns HAL_BUSY when you call HAL_UARTEx_ReceiveToIdle_DMA, then the interrupts is not enabled and you'll never get an interrupt on any new data received.

What you should do is set a error flag and check the flag outside of the interrupt. If set, then try to enable the HAL_UARTEx_ReceiveToIdle_DMA again. See code below

void HAL_UARTEx_RxEventCallback(UART_HandleTypeDef *huart, uint16_t Size) 
{
	if (huart->Instance == USART3) {

//memcpy(MainBuf,RxBuf,Size);

		oldPos = newPos; // Update the last position before copying new data

		/* If the data in large and it is about to exceed the buffer size, we have to route it to the start of the buffer
		 * This is to maintain the circular buffer
		 * The old data in the main buffer will be overlapped
		 */
		if (oldPos + Size > MainBuf_SIZE) // If the current position + new data size is greater than the main buffer
				{
			uint16_t datatocopy = MainBuf_SIZE - oldPos; // find out how much space is left in the main buffer
			memcpy((uint8_t*) MainBuf + oldPos, RxBuf, datatocopy); // copy data in that remaining space

			oldPos = 0; // point to the start of the buffer
			memcpy((uint8_t*) MainBuf, (uint8_t*) RxBuf + datatocopy,
					(Size - datatocopy)); // copy the remaining data
			newPos = ((Size) - datatocopy); // update the position
		}

		/* if the current position + new data size is less than the main buffer
		 * we will simply copy the data into the buffer and update the position
		 */
		else {
			memcpy(MainBuf + oldPos, RxBuf, Size);
			newPos = Size + oldPos;
		}

	}

	print_mem_hex(RxBuf, Size);

 UART_EnIdleDMA(huart);

}


int errorFlag;

void UART_EnIdleDMA(ART_HandleTypeDef *huart)
{
 if(HAL_UARTEx_ReceiveToIdle_DMA(huart, RxBuf, RxBuf_SIZE) != HAL_OK)
 {
 // set error flag. Check error flag in main loop and call HAL_UARTEx_ReceiveToIdle_DMA again later.
		errorFlag = 1;
 }
}

void UART_CheckIdleDMA(void)
{
	if(errorFlag)
	{
		errorFlag = 0;
		UART_EnIdleDMA(&huart2);
	}
}


int main(void)
{
	// other HAL code

	while(1)
	{

		UART_CheckIdleDMA();

	}

}

Also should avoid doing memcpy and print routines inside an interrupt as it will prevent other interrupts from firing. You'll want to re-enable UART interrupts and exit right away. That way you don't miss any new packets of data. 

See my github code https://github.com/karlyama**bleep**a/Nucleo-L432KC_UART_DMA_HAL_status 

It shows how to deal with HAL status. It also uses a ring buffer to save the received data to. Because I use pointers, there is no need to memcpy the data to a buffer. The DMA knows which index of the buffer to save each packet of data to. 

UART_Parse function shows how to then get each packet and parse it.