It really depends on the two people involed as to whether they grow fonder or wander. Generally speaking "long distance relationships" are meant to be (temporary). The goal for most couples is to be in the same home or town at some point. (LDRs are usually the result of circumstances and not choice.)
The best LDRs are those with a deadline for when the couple will be together permanently. The people involved also take turns visiting one another frequently and have contact throughout the day via phone, email, skype/webcam....etc
Having said that if a couple is young for example just graduated from high school and attend different colleges... odds are they will end up splitting. It takes a lot of maturity to be in a LDR. Eventually students socialize with those on campus, pleding fraternities/sororities, which often leads to froming new relationships. Young people also usually lack the finances to travel frequently to visit one another.
Another major challenge is when the couple has disagreements. It easier to ignore someone when you are angry in a long distance relationship and it much harder to "make up" without physically being able to hold one another.