So I am using the TVout library, though I'm not sure you need to know much about it to solve my problem. Basically the arduino program works for about 1 second then shuts off. Is this a serial overflow or something?
What do you mean by "shuts off"? Does your program seem to stop running or does the Arduino board actually manage to power down?
if (Serial.available ())
TV.draw_circle(Serial.read() - 6, Serial.read() - 6, 6, 1 );
You should really be checking that Serial.available() is greater than 0. While syntax is correct, you should keep in mind that Serial.available returns the number of characters in the serial receive buffer.
As AWOL points out, you are calling Serial.read() twice. Each call to Serial.read() removes 1 byte from the buffer. So if there was only one byte in the buffer, the 2nd call to Serial.read() will result in -1.
Either you meant to read 2 bytes in which case you could wait until (Serial.available() > 2), or you wanted to use the same byte twice in which case you should create a variable like char byteIncoming = Serial.read().
There really is no reason to call Serial.flush(). And as of 1.0 flush actually flushes the transmit buffer, not the receive buffer.