Hello Jeff,
It sounds like you are running out of voltage, but not necessarily battery capacity.
If you were to get too close to fully depleting your battery then you'd expect to run into the ESC's low battery cutoff (LVC) at maybe 3.4V per cell.
On the other hand, if your combination of running RPM times Kv is a voltage that is too high a percentage of the nomuinal battery voltage, then your ESC governor loop could run out of voltage headroom, and you'd drop out of regulation and lose power ... but not necessarily trigger the LVC.
Remember that we typically lose ~ 1V in resistive losses.
What is your motor Kv, cell count and actual running RPM? That is, tached, not the setting.
take care,
Dean P.