97 Civic Sedan AT reverse won't engage
 

A week ago, I noticed my 97 Civic Sedan AT reverse gear won't engage. Once I put it on gear, it makes a slight nudge moving backward but applying gas just revs my engine up without getting the vehicle to move back faster. The car is still able to barely move in reverse in level smooth pavement but it will refuse to move back in any kind of downward incline or rough terrain and will just rev up my engine.

The shop recommended I flush my automatic transmission fluid which I did. They ran the car afterwards but the reverse problem did not change and was not fixed. I'm afraid my problem is much deeper than the fluid, which I admit I might've neglected to replenish sooner than I should.

Can anyone give me any insight as to how much damage my transmission may have sufferred? I'll have it re-estimated for damages soon but I'd like to get some advance advice from you guys first so I don't get ripped off by an overestimate.

Thanks in advance!