FBI statistics report that 67 percent of murders have been solved since 1980. The other 33 percent go unsolved as a result of lack of evidence, lack of witnesses, witnesses who refuse to cooperate, lack of motive and geographic location.
Lack of Motive
Some murders have a clear motive. When a cheating spouse turns up dead, the other spouse and lover are prime suspects. When a gang member's body is found in a rival's territory, the rival is the likely offender. Some murders, however, have no motive. If someone with no criminal ties and no enemies is murdered, it is difficult to ascertain the reason. When that happens, the case is more likely to go unsolved.
Lack of Evidence
Investigators rely on evidence for identification and conviction of the murderer. If evidence is lacking, it is difficult to make a case, even if you establish clear motive. The murder weapons, footprints, tire tracks and DNA (hair, saliva, blood) are all useful in catching the killer. The less evidence found, the more difficult it will be to capture the murderer. Even if the authorities apprehend him, it will be difficult to convict him.
An eyewitness testimony can truly solidify a case when combined with strong evidence and clear motive. The problem is many murders occur in isolated areas without witnesses. Even if a person observes the crime, he may be reticent to come forward out of fear for his own safety. The notion of testifying in open court when there is a chance the suspect can be released is frightening. This fear of reprisal can lead to a witness abstaining from testimony, which can ultimately leave the murder unsolved.
Large cities tend to have higher incidences of unsolved murders than small towns. Although less populated areas can have unsolved homicides, the greater population of big cities can make it difficult to narrow down suspects. Areas with high crime rates are even more likely to have a higher number of unsolved murderers. Combine this with police forces that are often spread thin due to the high crime rate and outside factors such as budget cuts, and you have an area where murders are likely to go unsolved.