If the cellis producing at first then stops because it thinks there is not enough salt, then the problem is most likely just the sensor, and that should be replaceable all by itself, (I don't really know since I haven't had one to actually look at yet.
Again, I am not sure but it very well could be that the sensor is just bad, OR the part of the circuit board that is using the sensor input to tell the rest of the system what is going on could be bad, and that could very well be an intermittent blown fuse, (it works until it gets hot then separates, and when you turn it off it cools and makes contact again, and works until it gets hot), I have seen fuses do this many times while working with automation and robotic machinery, (they are a royal pain to track down), but I have also seen solder joint on circuit boards do the same thing.
Power transformers can also act like this, or even a bad connection somewhere.
I suggest you just see if you can remove to sensor and have it tested, or buy a new one and try it, that should most certainly be cheaper than the cell, I am guessing here but I think the sensor would work on the idea of measured resistance, or measured voltage or current, comparing what is sent out versus what returns, and the controller compares the 2 values and decides what the salt level is from that.
If the sensor tests good or a new one does not resolve your problem then I would look at the controller, and I would really find out some how or another which wires go to which wires, one set has to be for the cell and the other for the sensor.
If the sensor is bad, then replace that, and make proper repairs, (solder), the wires, so they are making the best possible connection.
One way to check the cell itself is to turn the SWG off, and run the pump, get a water sample as it comes out into the pool, as close as possible, and test it for CL, then turn the SWG on and take another sample the same way and see if the CL is any higher, if so then you know the cell is good, or if you have a way of getting a water sample before it enters the pool would be even better.