OP has not said if their car is automatic or manual. The automatic transmission in the 2001 Civic, which is probably similar to the CRV, has a reputation for short life.
On the other hand, in a manual car when you are in a gear and press the gas pedal past a certain point to have the rpm's suddenly jump up without the car going proportionally faster, that is simply a worn out clutch.
On the other hand, in a manual car when you are in a gear and press the gas pedal past a certain point to have the rpm's suddenly jump up without the car going proportionally faster, that is simply a worn out clutch.