The ADC shouldn't stop responding unless it gets a large voltage surge on one of the inputs but that would have to be more than 5V to go beyond the maximum input limits.
The ADC Differential Pi class has a timeout variable which keeps checking the ADC to see of a sample is ready and it could be possible that for some reason the ADC is not reading a sample before the timeout occurs which may be causing the program to hang.
In the ABElectronics_Win10IOT_Libraries folder there is a ADCDifferentialPi.cs file which contains the class and methods for the ADC Differential Pi. On line 252 is the timeout variable.
var timeout = 10000;
You could try increasing the timeout value and recompile the dll to see if that has any effect on the stability of your program.
One way to work out if it is a software or hardware issue would be to set up a separate SD card with Raspbian linux and try using one of the readvoltage demo in our Python library to see if that can read from the ADC Differential Pi without failing.