I use my remote control every year at Christmas for about 2 months, always with the same battery, which I then of course take out for storage until the next Christmas. I have about 6 different fairy lights that I control with it and no problems.
Maybe a battery problem after all? With the button batteries, it is important that you do not touch the two contacts together, e.g. do not hold the poles between your thumb and index finger, as this will quickly discharge the battery.

Runs smoothly, right from the start! So unfortunately I have no advice, sorry!