Summary
We have 6 TPS92515As controlling 6 LED strings, arranged in a grid, and tightly packed.
When we turn on 1 TPS92515A and maximize the output current (no PWM) to the adjacent LED string (only the Red it appears) begins to operate like a photodiode and generates a small voltage across the string.
This voltage appears to be enough to disrupt the TPS92515 circuitry, apparently forcing it into UVLO mode.
Per your request we have assembled various scope traces and their respective situations.
In all cases below the two scope traces are on the Red (offending) channel and its associated TPS92515.
Base test - Red is full on. No problem.
Everyone Off. No problem.
Mint On 10% PWM - Red Off. No problem
Mint on 10% PWM - Red On. No problem.
Mint On Full, No PWM. Red can no longer work.
Mint Off. Red Fine Again.
Here, two channels supplying light causes a failure. It was arranged so that either of the two channels individually did not cause the Red channel to die. But the two in combination did. This appears to eliminate the idea that a single channel is causing it.