TVS Array Clamping With IO Less than Standoff Voltage
The datasheet has been silently updated: 

TI document SLVSD85–NOVEMBER 2015 shows one orderable device, TPD4E02B04DQAR, with a minimum activation voltage listed as 6.7v and no further details.

TI document SLVSD85A–NOVEMBER 2015–REVISED FEBRUARY 2016 shows the same device, TPD4E02B04DQAR but with much more detail. It lists a lower minimum activation voltage of 5.5v. In section 6.3 Recommended Operating Conditions, it lists \$V_{IO}\$ Input pin voltage as –3.6v to +3.6v and the same with \$V_{RWM}\$ reverse stand-off voltage.

Since these TVS's are ground-referenced, whichever one(s) are conducting must be experiencing a spike beyond +/-3.6v. The \$V_{BRF}\$ and \$V_{BRR}\$ Forward and Reverse Breakdown Voltage (any IO pin to GND) is specified as +/-6.4v nominal, but could be as low as +/-5.5v. 

So there must be a spike beyond +/-5.5v on the affected lines. If you use an oscilloscope to probe them, be sure to use a 10x or even 100x probe for greater bandwidth and reduced loading. A fast 'scope may be needed.

Short of that, you could try temporarily adding a little capacitance to these lines to prevent a fast spike from tripping them. Something like 20pF might do it. Of course, this will slow down fast data edges, so if high-speed data is on those lines, it may be affected.