It is difficult (but not impossible) for someone to survive on their own for a long period of time. An extra pair of eyes, hands, and ears will greatly improve their chances of survival, even if it's only one other person. If someone must survive on their own, they should make sure that they have plenty of things that will help ensure survival.
Along with the deficiencies that go along without help, skilled or not, there's the small possibility of developing psychosis due to lack socializing if one's mental health is questionable prior to the zombie apocalypse. However, the greatest danger present is the lack of information. One survivor, especially one who wanders without a set destination, is not only unlikely of finding help, they're unlikely of finding resources or any other specific knowledge about world events, due to not encountering other humans on a regular basis. For example, a loner may think that a zombie apocalypse is still going on, even after it had burned itself out.
Going deeper into the choice of living alone, any survivor choosing this path would have to live a hunter/gatherer lifestyle. This isn't a problem for the few enclaves of hunter gatherers around the world who maintain their hunter gatherer traditions, but the average person who choose this lifestyle are going to find themselves dead from lack of food, killed for attempting to steal food, or dead because they ate something that isn't edible. Survivors who decide to become loners have to learn to feed themselves in ways that don't harm or hinder their ability to survive alone.
Most areas of land prior to the rise of farming were made up of inedible organic matter (trees, grass, wild poisonous plants, etc) which is why many early civilizations were near the ocean, because it's the only place that could match a farm in food production.
There is also the matter of finding a place that can provide adequete protection and can be defended easily. This will be impossible for one person, as even with a security system, they are still their own "first responder" and will have to solve all problems by themselves. Staying in one place would be incredibly dangerous, as they lack the manpower to fight a group of anything and the knowledge to do everything that would be required to put up a respectable fight. Even with the tactic of running away to fight another day, they run the possibility being followed.
It is possible to survive against attacks by crazed survivors using guerilla tactics. Find books on guerrilla warfare (such as Sun Tzu's Art of War), these type of books give great knowledge on how to win battles using cunning and intelligence over brawn and overwhelming numbers.