Why does Earth enjoy a significantly longer time as a habitable planet as compared to Mars or Venus?

By survived, do you mean remained habitable?

If so, then there are several reasons:

For Venus, the problem was that it was just barely on the edge of the habitable zone when the Sun was younger and less bright. As it aged and brightened towards the values we see today, any oceans began to evaporate. The resultant water vapour is a very powerful greenhouse gas, and so would have trapped yet more heat, causing a runaway greenhouse effect, until it is the baked, hellish world we see today.

Mars, on the other hand, was believed to be too small. It (probably, assuming modern theories are correct) started off as another habitable world, but since it was smaller, it would've had less residual heat left over from its birth, and would've cooled quicker. This would've caused the core to solidify, removing the magnetic field. This meant that the atmosphere was vulnerable to the solar wind, which would've gradually blown it - and any warming greenhouse gases - away, and with the lower pressure, the water would evaporate away as well, rendering Mars uninhabitable.