Why can't the Tucks stay in any one place for very long?

I believe that this question is asking about the book Tuck Everlasting.  
The Tuck family can not stay in one place for very long because other people would eventually become suspicious of the Tuck family.  The entire family is immortal.  They have stopped aging.  If they were to stay in one place for a long time, people would begin to wonder why nobody in the family ever appears to age.  The Tucks could probably get away with staying in a single place for a decade or two, but after that it would be fairly obvious to other townspeople that something is definitely different about the Tucks.  All of this is explained to Winnie (and readers) in chapter 10.  Mae admits that they have been in their present location for about as long as they dare stay anywhere -- 20 years.  

"But they can't stay on in any one place for long, you know. None of us can. People get to wondering." She sighed. "We been in this house about as long as we dare, going on twenty years."