Often times there are jobs that provide value at an hourly rate greater than $0.00 and less than whatever the minimum wage is at. The job could be done, and provide meaningful value, so just because it isn't worth paying a minimum wage doesn't mean the job shouldn't be done at all. It's a difficult situation because the employer wants to pay the worker a fair value for the job, but the government forces them to pay more than the fair value of their work. That's a poor moral and financial situation, and so businesses look for people in other countries, or technology to automate the job completely.
The trouble with increasing a minimum wage is that it increases the reward for whichever entrepreneur is able to automate that job function, which would further income inequality in the long run by causing job loss of all those workers.
One question I have is why do we care so much about protecting minimum wage jobs? If no one had the safety net of a minimum wage job, they would be forced to innovate and pursue groundbreaking research in other fields - such as medicine or technology. Imagine if the rate of innovate was exponentially increased - think of the thousands of lives we could save or the decrease in costs of healthcare if we said "no one can work at Starbucks - you have to be a doctor."
source: http://inflationdata.com/Inflation/Inflation_Rate/Long_Term_...