How to tell if the battery in my 9-3 is due for a replacement?

Ok my car has been acting crazy since i changed remotes. I can lock my car with the remote but come back 5 mins later and neither remotes work. Now I have steering wheel lock malfunction and key not accepted when there is no key in the ignition. It did this 8 months ago but I fixed it by resetting the battery. I tried that just now for 2 hours and its still doing it. Car starts flawlessly but I am not sure if its the original battery.