My 2007 GMC Yukon has 120,000 miles. Recently, I noticed that when driving the vehicle, the RPM do not drop, or reset, as the car accelerates. Instead, the faster the car goes, the higher the rpm's go, and it feels as if the car is not changing gears. What could this be?

You have a failed transmission that will have to be
rebuilt or replaced with Reman

The flair in the rpm & gear change issues, should
have been the clue

How does that happen on a 7 year old vehicle ?

You fail to change your transmission & power steering
fluids every three years & those items that should last
15 years & 150,000 or possibly more, are given a death
sentence.

Trans fluid breaks down from heat in about two years &
like all fluids the additive packages are used up

Brake Fluid --every 2 years
Spark Plugs --every 3 years or they wear & stress the
ignition system

Motor Oil-well-you do as you please

I change mine 3 times a year,which is about 4,000
miles
When we worked-four times a year

I have a 2014 vehicle that I got in march
Changed the oil this Monday at 711 miles
WHY- it has been in there 4 months (remember
3 times a year) BUT --i keep my vehicles 18 years

I have one that I have had 30 years

The trans fluid --I will be doing soon
WHY- because I once owned a trans shop
& know what wears & when

Most wear,you ask-yep-the first thousand miles
& this vehicle has NO Filter,just a screen