The patch does wear off but the main reason is because there's a finite amount of enzyme (glucose oxidase) on the filament that does the actual glucose measurement on the sensor. So over time the enzyme is "spent". That, and of course it's lucrative. There are clever ways people have come up with (particularly from low income regions) where you can trick these sensors or the apps to reset and apparently you can get way longer lifespans like that (for the dexcom you also have to file down the bluetooth transceiver so that you can get at the battery within) at the risk of no longer being able to trust the readings.

There's one company that's experimenting with an implantable CGM that will supposedly have a 6 month lifespan, with a bluetooth powered patch that you apply on the skin overlying the implant.

All CGMs only work for a period of time, like a couple of weeks or so. Then you get a new one. To keep the size reasonable it can't be too big.