Why did Great Britain repeal the Stamp Act?

The simple answer is that it was becoming virtually impossible to enforce. The Stamp Act had been a hugely controversial piece of legislation right from the start. As well as being yet another example of the colonists' main grievance—taxation without representation—the Stamp Act was designed to raise revenue to pay for a standing army, something that American patriots regarded as a potential instrument of tyranny and repression. To add insult to injury, the Stamp Act greatly increased the cost of paper, thus making it more expensive to buy the newspapers and pamphlets that were the main source of revolutionary ideas.
Not surprisingly, the Stamp Act led to complete uproar in the American colonies. A campaign to boycott British goods immediately got under way. Furthermore, riots and other disturbances regularly broke out, which became increasingly violent and bloody. Unless the Stamp Act were repealed, the American colonies threatened to descend into outright anarchy, and that wasn't something the British were prepared to contemplate.
The general mood in Parliament was for repeal, and after the eloquent testimony of Benjamin Franklin, the Stamp Act was doomed. Before the House of Commons, Franklin testified that were the Stamp Act to remain in force, the Americans would lose all respect and affection for the mother country, with potentially disastrous consequences for commerce between Great Britain and her colonies. Just over a week after Franklin's testimony, the House of Commons voted by a large majority to repeal the Stamp Act, handing a huge victory to the American colonists.