This actually happened in the 1960 version as well. In both cases, for the earlier parts (when he's traveling to the "near" future), the time machine was placed in the house of the Time Traveler, and even though the house was abandoned for many years, it was never torn down. At best, it was boarded up and abandoned. It's quite possible it was just a matter of luck that the Time Machine never had anything get in its way during the early sequences of time travel.
In both movies, these short time travel sequences ended with a longer trip to the year 802701. In the 1960s version, the Time Machine is covered up by rocks, which presumably erode away through weather, in the 2002 version, the Time Machine is actually in the open, the Time Traveler can see the effects of erosion occurring around him. In both cases, continental movements probably would have dropped the Time Machine into the ocean by 802701, but that would have resulted in a much shorter movie.
In the end, both movies were based off the book written in 1895 which was an allegory about class division of the time, and the exact mechanics on how a time machine would need to work weren't exactly thought out. The best explanation is probably that the time machine has a built-in safety mechanism that prevents it from coming to a complete stop unless it has a clear area around it, and it somehow sticks to the surface of the Earth while moving (let's blame gravity for that one).
Fun fact: there was a 1978 made for TV adaption that ignored the whole "the machine stays in the same place the same time" which had the hero travel to the 1692 Salem witch trials and the gold rush in 1871.