Sounds like a 433mhz ISM design, I have several remote relays that also use a simple wire antenna. I agree just soldering a longer piece of wire on isn't likely to help.
Question is, is it really just a simple piece of wire (hopefully of the correct 1/4 wavelength length), or is it just the end of a coil antenna, and the coil is inside the box somewhere.
These instructions look helpful:
ClickyCan you get inside the control box to inspect the rest of the antenna?
Other than that, just make sure the wire is as straight as you can make it, maybe use a piece of plastic tubing to keep it that way. Try moving it to different orientations, out, down, sideways, etc.
2013 KZ Sportsmen Classic 200, 20 ft TT
2020 RAM 1500, 5.7 4x4, 8 speed