Try this - UNTESTED
bool printingOK = false;
void loop()
{
currentTime = millis();
if (Serial.available() > 0)
{
char recentChar = Serial.read();
if (recentChar == 's' && !printingOK)
{
printingOK = true;
previousPrintTime = currentTime;
}
}
if (currentTime - previousPrintTime >= 2000 && printingOK == true)
{
SerialMonitor();
previousPrintTime = currentTime;
}
}