Transmission works intermittently

One morning, I started my car but the car wouldn't move in any gear. I could feel the transmission change change gears as I moved the shifter. The RPM's would also drop when it was put into gear. I had it towed to the dealer. The dealer determined, "No codes in the TCM. Verified vehicle does not move, all sensors are reading. Fluid is full. Put vehicle on lift and the wheels will turn when there is no load. There is a failure in the transmission. Transmission needs to be replaced. The dealer gave me a quote for a re-manufactured transmission, $3,492.99.
I went out to the car to wait for the tow truck. I started the car and it shifted perfectly, like it was brand new. I drove it for about a week but, one day, while driving about 45 mph, the car lost power. I was able to coast into a parking spot but now the car has the same problem.
Do you have any suggestions as to what could be the problem?