I have the same issue with my XL. Seems to be overheating because it takes about 30 minutes act up and usually only after using patches with high DSP usage. Switches 2, 3, 5, and 6 are frequent problems, but 1 and 4 act up some times. If I shut it off than back on almost immediately, the touch function works again, but the problem comes back faster. The unit is a little warm to the touch, but no more than my phone and less than my laptop. It looks like the only air flow is throught the 1/4" jack, so I wonder if a problem is more likely with more cables plugged in. It's less than a week old, so it's going back to GC rather than messing with the warranty process. Hopefully they will have a replacement that doesn't have the problem.
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Ok, this is taking an unexpected turn. I went back to GC and exchange my XL. Straight out of the box (Ver 3.02), I added some blocks to a preset to max out the DSP, played a while, left it on for a while with my singles coils humming away, played more, left it more... 5 hour later, I could not replicate the problem. Great I thought, and updated to 3.15 and set it up for normal use, and about 45 minutes later, the problem was back. After testing for a while, I realized that if I pressed the switch to turn the block off and back on and switched to another block where touch was working, the function returned to the previous switch. The one change I made that seemed related was in global setting, I had changed "Select Stomp" from the default of touch to both touch and press. I switched it back and initially nothing changed, but I rebooted and after 5+ hours, the problem seems to be gone. I know I changed the setting in the previous unit and I'm 99% sure I left it on the default in my test of version 3.02. I'm assuming this is a software bug rather than a hardware problem, but the exact cause is probably more complicated than just high DSP use and a setting change, otherwise there would be more complaints and questions.
I'm going to reported as a bug and hope that Line 6 can replicate the problem.