Here is a little bit of an update on my quest to find out why our auto tranny's are behaving in this manner.
First off, I removed the kick panel so I could get at the ECU so that I could see if it would give me an error code. It did not. It gave me a code of '55', which means no error.
Next, I went and talked to a auto tranny specialist here and we talked about this shift problem in great detail for over an hour. He was very informative. He seems to think that this is definitely an electrical problem and not a mechanical one because of the fact that it always happens during the first 5 to 10 minutes of a cold start.
He advised me to splice an LED on the wire that goes to the Shift solenoid for D1 to D2 (this is pin 6 of the TCU). I believe the service manual calls it Solenoid "A". Tie the other end of the LED to ground. Make the wires long enough for the LED to be in plain site while driving so you can see it for this test.
When the car is operating correctly, and the car is still in first gear the LED will be 'ON' and when it shifts to second gear, the LED should turn 'OFF'. Now, if the car doesn't shift into second and you are above 37 MPH, look at the LED as it should be off. If the LED is 'ON' at this point, then the TCU is bad. If it is 'OFF'and your car hasn't shifted yet into second, then more than likely you will have a bad shift solenoid for D1 to D2.
I told him that I had read that on other forums that replacing the valve body was a fix that some people had tried and worked. He told me that the reason that was probably a fix is because more than likely, when the valve body was replaced, so was the solenoid because it is attached to the valve body.
The reason that we are seeing this intermittent shift occur during the first to second shift interval is because this solenoid is used more than the other solenoids. However, in time the other gears will more than likely behave in this manner, which means that the other solenoids will eventually go bad too.
I haven't hooked up the LED yet. The TCU is a little bit further up in the dash and so I really haven't had time yet to unbolt it from the frame. I'm doing that this weekend, so when I get the results of the LED test I'll let you know. If the LED is 'OFF' and the car doesn't shift, I'm taking the car to my tranny specialist and he is going to remove the D1 to D2 solenoid and test it in a heat exchanger to see if it is operating properly.
I'll let everyone know as soon as I know...!