Interesting thing in the design of the whole setup is that the laptop has a power supply followed by a DC power filter in a seperate enclosure. This gives me an impression that at the last moment they found out that noise from the input was unacceptable. Might this affect the touch in any way?
PSU noise certainly could affect the touchscreen, though it's highly unlikely this would be in a way which gets worse over time. I'd expect it to either work or not work.
More than likely, they designed the product without the filter, went EMC testing, failed, and had to come up with a fix at the last minute. That's the usual reason why ugly, obviously bolted-on filters end up being used in products.
It's easy to test, though. Run the laptop until it starts to misbehave, then pull out the power lead and run it off the battery for a while. If it still misbehaves, then it's not power supply noise. (At least, not noise from the external adapter... it could still be internally generated noise, but there's really no good reason why this should change with time).
Does it make any difference what the state of the battery charge is? Some mains supplies are actually quieter on full load than they are on part load. Charging a flat battery might cause more current to be drawn from the mains supply, which would put it into a quieter state. As soon as the battery is charged, the current draw reduces and the adapter gets a bit noisier. Highly unlikely, but not completely impossible.
What happens if you power the laptop from a different supply? Could you power it from a quiet lab supply?
I wonder whether there's some ongoing self-calibration going on which is eventually failing. There must be a sensitivity setting somewhere in the system; maybe there's a periodic calibration being carried out which is affected by temperature? When it starts to misbehave, stick it in the fridge for half an hour and see what happens.