Shakespeare was a master of characters and taking old stories and revitalizing them. He was also an inventor of words, many of the terms he uses were not in the common speech. His mastery has not changed. It could be argued that the modern play is more poignant and the choice of dialect more understandable, but that doesn't effect Shakespeare's position as the greatest writer of the renaissance period and a continuing source of inspiration to modern playwrights and poets.
No, Shakespeare has not lost his appeal. His work will forever remain a classic as it they are so original and iconic, and completely relevant - even in today's modern society. The lessons that he teaches through his plays are some which are applicable to most people. His works will always be taught in English classes across the world and many people enjoy his work.
Shakespeare is alive and well across the country. Look at any college summer play schedule and you'll likely find his works as one of the summer theater offerings. Still known and studied for his prose, statements on humanity or lack thereof Shakespeare carries a valid weight of respect and knowledge. While not Broadway making millions, he continues to inspire from the grave without compensation.
Shakespeare was a genius. He wrote many timeless plays and stories. I don't believe that they will ever lose their appeal. The stories he wrote are about situations that can be transferred to any country, any century, any group of people. The underlying themes are those of human nature and transcend the time period. His plays are always appealing to watch or read.