If demand increases, why dont sellers offer more for sale at the SAME PRICE?

Why, when people will pay more for each one.

Maybe more aren't available. Maybe they are selling more, but selling them at a higher price.

The object of being in business is to make a profit.

That means you have to work more to make the same amount of money. If you raise the price then you can make more without working more.

As demand goes up, price goes up because the sellers know that they have a hot product that people want. If you want it bad enough, you will pay more.

At some point, there will be an equilibrium price where things will balance out. If the price goes above that, demand will drop off. If the price is too low, demand will continue to outstrip supply.

Example: the Nintendo Wii
The retail price on these is $250 and more people want them than can find them.
Demand is higher than supply. When this happens, people are willing to pay more to get one so you see people spending $400+ on Ebay to purchase one.

Example: Brown Zune
Not sure on the price but they did not sell well. Supply is higher than demand so you see stores dropping the price to get rid of them.

For every product, there is in equilibrium price where the supply curve and the demand curve will intersect.....which means there is a price where people will buy the items at a frequency that the supply can keep up without having too many extra.