No reverse a.t. trans do not think its burnt just quit backing up one day

If the oil is not cherry red or smells burnt then there was not an oil change done
for oil to burn in such a short time, you would have had indications of problems early on and not a few days later.
for transmission problems run the fault codes as they will give a good indication of problems that are repairable
If you are still worried, have an accredited transmission shop do a pressure test , band and clutch pack adjustment and a filter clean ,then fill with new oil. The pan will be off to do the adjustments and filter so any major failure will be noticeable at that time.

check the trans for fluid with the engine running and the trans in park with the emergency brake set. If the fluld is not up to the cold mark or is dark when you wipe it on a paper towel - it should be pink and oily, not brown/black with a burnt smell. If it is not at the cold mark by quite a bit, add half a quart of the fluid specified for the car. Try going into reverse after you do that.
If the fluid smells burnt, is dark and thin, have the fluid changed. Best to pay extra to have it pumped out and then refilled and the screen/filter cleaned at the same time.

Good luck.

Sounds like the band in the transmission is burnt up.

transmission is burnt up do to fluid being low and high milage.Check fluid if color of fluid is a brownish color the clutches are burnt up.

if it smells burnt it will need that rebuild but thats because the pump did go now u have burnt up the (bands)as they say/nothing to check that i can think of just time to pull trans

Are you getting a check engine lite? Whether you do or don't scan for codes, and follow up from there.
But I think you may have to have TCM reprogrammed.

Sounds like a typical reverse band problem...cover the easy things first however... is the fluid full??? check it engine hot in park....is the fluid burnt??? bad smell not red like out of the can... if its low or if its burnt make sure you purchase the proper fluid for your particular vehicle some trans fliuds dont mix...a trans service may fix it as the trans has a filter that (may) be clogged but usually this causes a non shift in drive as well as reverse...if all else fails sounds like a trans repair/replacement is in the horizons.Cost factors: Trans fluids $3.00 qt.: trans service $30.00-$100.00: Trans repair/replacement $600.00-$1500.00.

check link to trans to see if is working when you select it to reverse are could be trans pump in the trans may need to rebuild the trans

Presuming the fluid level is full,it is quite common for a broken reverse sun shell to give the symptoms you are experiencing,as well as some other areas that could also give similar symptoms such as burnt clutch packs,or the torque convertor going bad,and eventually the vehicle will stop pulling altogether.If the fluid is full,the problem is pretty much going to require trans removal and repair.Further diagnostic would include installing a mechanical oil pressure gauge onto the transmission to monitor main line pressure and see what it's doing while the trans is acting up and not pulling,and this does require a gauge capable of handling 300 psi.Also pull diagnostic trouble codes from the vehicle computer (PCM).Good luck.

yes...i would pull the dipstick to check the color of the tranny fluid or smell it if it smells burnt you will know i am assuming that it is automatic