Hi Cyril,
None of our reference designs have any ESD protection on resistive TS lines. As I see it there could be two possible causes - capacitance added by the ESD device and leakage current. In my opinion the problem is caused by the device capacitance (60 - 80pF, compared to the AM335X input sampling capacitance of 5.5pF nominal).
I can't say about software behaviour.