Thank you for the information Jing. I have made modifications to my board by removing all of the non-essential components required for programming. All that remains is the MCU, 10k pull up resistor on the reset pin and a 0.1 uF decoupling capacitor for the MCU power pin, along with the traces leading to the SWD programming connector, i.e. only parts related to the SWD interface. I am still unable to program the MCU at supply voltages below 2.7 V, unless I first halt the processor using the Kinetis Recovery Tool. I only have success without using the Kinetis Recovery Tool with voltages above 2.7 V.
The MCU I am working with on my board was ordered from our CM back in June of 2018. If I try a simple breadboard setup with an MCU that was ordered over two years ago, I do not have an issue programming at voltages below 2.7 V. Please note that the breadboard setup and my PCB setup are similar in nature now that I have removed all non-SWD related components.
I am suspecting the core is going into an infinite reset once it detects the supply is below 2.7 V based on Table 7 of section 2.2.2 of the KL03 Reference Manual.
-Andrew