You need to append to the text box, not change the text.
port->Open();
StreamWriter^ sw = gcnew StreamWriter("GPSdata.txt");
String^ txt = port->ReadLine();
TextBox1->Text = txt;
while (( txt = port->ReadLine())!= nullptr) {
TextBox1->Text += txt;
sw->Flush();
}
Also make sure the text box is multiline.