Why did the disciples die?

In my last Sunday school class (4th and 5th graders), we looked at the disciples. All except John are believed to have died a martyrs death. These men died because they refused to say Jesus had not risen. A few students had hard times with this. Why didn't they just say they had not seen Him?

Why die just to say that they had seen Him?

First, they were being obedient to Jesus:

Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, (Matthew 28:19)

Second, they felt compelled to go by the love that Jesus had taught them and shown them:

“For we cannot but speak of what we have seen and heard” (Acts 4:20)

Third, they did it for you:

"By this gospel you are saved...that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures, and that he appeared to Peter, and then to the Twelve. After that, he appeared to more than five hundred of the brothers at the same time...(1 Cor. 15:2-6)