Those switches only connect on the analog side so that shouldn't affect the ability to program the part.
I have 2 theories based on some of the information you provided.
1. seeing as for 1 of the boards you were able to mass erase the part with ARMWSD and then you were able to reprogram using keil, I suspect that something in the code could be locking up the part or disabling the JTAG.
What does the code you have on the part roughly do?
2. Some part of the circuit is damaged which causes the part to not power up properly or run properly and the switches alleviate the issue by providing alternate power paths (just a stab in the dark). If you program a simple blinking program and then put the switches back in the state they were when you couldn't program, does the blinking still work correctly? If you scope the power, gnd and decoupling pins when the board can be programmed vs when you can't program it, do you notice any differences?
When your board was failing to program was there external circuitry attached to the board?