L298N Module Out 1 and Out 2 failure
I have an L298N motor controller module, rated at 5 amps.


In the opening blurb on page 1 of the data sheet it says the L298 can supply a total DC current up to 4 amps.

In the table for absolute maximum ratings it says that the DC current is 2A. You can get 4A when both halves of the bridge work together i.e. they are not used in a H-bridge configuration but a parallel configuration.


  I'm using a current sensor per motor to learn when the motors have
  reached a high current load (~2.26 Amps) then stop them once they
  reach that threshold.


This will likely lead to early failue of the L298 - respect the data sheet. For \$t_{on}\$ of 10 msecs you can go as high as 2.5 amps - are you adhering to this?

The thermal data for the device is 35degC per watt - are you using a heatsink and what power are you likely dissipating. These are very inefficient devices and warm up very easily because their output transistors do not saturate to anything like a conventional BJT or MOSFET. I'd urge you to read the data sheet on this device and recheck your calculations.