Not "wearing out." One component may be changing value over time changing the threshold it senses as a touch.
Touch lamps can be temperamental. Dirt or humidity can change the characteristics - I don't know the type you are talking about but some lamps use a fiber or paper insulator between the metal shell (part you touch or connects to it) and power line connection to the lamp - humidity goes up lamp triggers because the paper is slightly conductive (exacerbated if you've ever spilled something remotely hygroscopic in it)
They can also trigger with fluctuations in the power mains - look for a coincident event like a heater switching on or lamp dimmer used or something else along those lines. Power outages or glitches are another cause of false triggers.
The things are too cheap to be worth fixing - and there's a shock hazard involved while troubleshooting it and again after it is back in use if the repair is less than safe.