The Chevy Impala's
4T65E transmission was said to feature an updated
Pressure Control Solenoid starting in 2003. This was a major issue in the 2000-2002 model years. But, there are still many people with the 2003MY vehicles that are experiencing the same issue as you. The vehicle may or may not already have illuminated a Check Engine Light due to the issue. Even if not, it most likely still has stored a fault that could verify that the
Pressure Control Solenoid is faulty. The trouble code for this would be
P1811 (max adapt, long shift).
The component is located behind the side cover of the transmission and should take ~5 hours for a quality mechanic to complete. It is a rather big job and involves lowing the front cradle to gain access. If you're not 100% comfortable with a job of this magnitude this then get the vehicle to a well known transmission shop.
Pressure Switch Assembly (It is possible that the you can get the switch separate from the entire assembly. That's something you or your mechanic can look into)