Sounds like it's stuck in limp mode. This happens when the system thinks there's something wrong.

Is the CEL or any other dash indicators on?

If you have a scan tool, check and see if there are any error codes.

 

I have the same problem with my Jeep Patriot. My mechanic said it's a mechanical issue in this CVT transmission - the belt's tension has weakened. I still don't believe that I have to replace the whole transmission.

 

Slipping belts are often caused by wear in the pump flow control valve.
You have to take the transmission completely apart to get to it, and there may be other issues too like damage due to the metal shavings caused by the belt slipping, so that may be why they're recommending a replacement.

 

Did anyone find the solution to this problem of the cvt not shifting?

 

In some cases it's a fluid and filter change, or maybe a new transmission.

 

did you ever get around to finding out what the issue was? If so what was it and how long did it take if you did it yourself?