Problems when accelarating above 60mph

My 97 Passat GLX VR6 lately has to downshift in order to speed up above 60mph. RPMs jump above 4K. It stays in that lower gear until I release the gas pedal once I reach 80mph. It then has hard time keeping that speed and will gradually slow down to 75 or 70. Then, when I try to speed up, it would downshift again. And so my ride goes on...
What does this sound like? Is this a trans problem or my engine is for some reason losing hourse power.
Should I keep this car or get rid of it until it totally breaks down?

Is your check engine light on?

No. There is no check engine light.

Does it tend to feel as though it loses power in any gear at high RPM's or the exhaust sound different or woooshing like the catalytic converter may be clogged?

it feels like it can reach 80mph only at high RPMs (over 4000). It has hard time accelarating gradually. Around 60mph when I stop on the gas pedal. It does nothing and then downshifts in order to speed up. So, the car feels like it has more power once the high RPMs are reached. It also won't upshift again until I release the gas pedal even though I reached 80mph and RMPs are at 4500. I am not sure if the exhaust sounds different. The whole engine sounds different once the RPMs jump up and the car finally starts accelerating.

The only other common thing I can think of that might cause similar symptoms is the Mass Air FLow sensor, which can be out of calibration. This would have to be checked with a VAG scanner or simulator. Since you say it sounds different it might be worthwhile to have someone check the catalytic converters and exhaust too.