When gas prices are high, wouldn't it be logical to raise the minimum wage rate?

No offense intended, but this question shows a lack of understanding concerning basic economics. One of the problems that we encounter with many people is that they think of employers as bottomless pits of money. Therefore, they can afford to pay their employees whatever society thinks they should. In reality, it's not the employer that pays the salaries, it is the consumers. People go into business to make money. (There is nothing wrong with this.) In order to make money, the businessperson must produce a product that people are willing to buy. Often, producing a product requires hiring people that will do the work of production. The salaries of these workers becomes part of the cost of production and, therefore, part of the price that must be charged for the product. If your raise the price you pay the workers, then the employer must do one of two things. He must either raise the price of his product or he must not hire as many workers.

So, raising wages for one group of people can lead to higher price for all. So, everybody needs a raise. Therefore, everybody has to raise the prices of their products to bring in the money to cover these raises. It is a positive feed back loop that is on of the causes of inflation.

Another argument that people use to justify government induced raises in the minimum wage is that people deserve to make a wage on which they can live. The problems with this argument are two fold. First of all, minimum wage jobs are jobs for people who lack the skills to do anything else. In other words, they are the jobs that are traditionally done by teenagers who are still living at home, or college student that are trying to supplement other sources of income. These are not the types of jobs that people are supposed to make a career of. They are not the types of jobs on which you are supposed to be able to support yourself.

The second problem with government mandated pay raises is that the benefits of such raises are fairly quickly wiped out by the inflation caused by the pay raises. So, in the end, they do nothing to help those on minimum wage. Sure the person is making more money, but that increased income doesn't buy any more.

One other thing, you put a condition on your question (viz., "When gas prices are high"). If we are going to raise the minimum wage when gas prices go up, does this mean that we should lower the minimum wage when gas prices go lower? It's a logical extension of your question. Personally, I am more in favor of letting market forces dictate wages than government regulation. If an employer doesn't pay enough to keep his employees happy, then they will seek better pay elsewhere. This will eventually force the employer to pay his employees more or go out of business.

*******************
"stevenweven: then let's raise wages and let market dictate which rich people can stay rich"

That's the point, government mandating a minimum wage is not going to ultimately change anything. The market will dictate who becomes rich and who doesn't based on skills, hard work by the individuals, and demand for those skills. All a government imposed raise will do is devalue the money.

*******************
"stevenweven: money would be devalued if ALL wages were increased, not just minimum wage."

A rise in the minimum wage leads to a rise other wages. When the wages of the unskilled workers goes up, then the skilled workers (unions) will use that as a justification to demand a raise as well. After all, aren't the skilled workers worth more. Also, as I wrote above, increasing the minimum wage means that the employers are going to have to raise prices to make up for the increase in labor costs. That means that everyone else's wages have to go up to make up for the increase cost. You can't just mandate that one group's wages go up without affecting the rest of the economy.