Generally, that's true. For example, Katrina weakened slightly after hitting Cat 5. The question is will Rita weaken from Cat 5 so early that it can conceivably get back there before landfall.
For anyone familiar with Houston, I-45 NB from NASA Road 1 to downtown is running at 283 minutes (and no, that's not a typo).
These things need warm water and an exhaust. They are basically heat engines.
Katrina weakened because it moved too slowly, eating up the energy in its vicinity and clogging up its exhaust pipe with its own fumes.
If Rita keeps moving along, it will not weaken.
Katrina ran into the cooler waters dumped from the Mississippi River. There is NOT a big river to chill Rita as she barrels into Texas.