At a minimum, you should re-string your racquet once before each season.
The Merchant Experts Re-Stringing Factors:
Frequency of play:
The more often you play, and the longer you spend on court, means the more often you will need to re-string. Player A plays twice a week for an hour each time, while Player B plays twice a week for four hours each time. Although they both play twice a week, since Player B plays for more time total, he will need to re-string more often than Player A.
Style and level of play:
A player hitting with lots of spin will wear strings faster than someone that hits a flat ball. Or, a serve and volleyer who likely only hits a few balls per rally will likely have to re-string less, compared to a strong baseliner who holds longer rallies.
String pattern of your racquet:
A more open string pattern (e.g. 16x15) means more string movement, more friction and thus a shorter string lifetime. While a more closed string pattern (e.g. 16x19) will allow the player to re-string less often.
Type of string and tension maintenance:
Strings come in two different broad classes - multifilaments and monofilaments. Multifilament strings contain, as the name suggests, many fibers. Although this construction produces a very soft and comfortable string, those types of strings do not typically last as long. They typically start to fray and are more susceptible to breakage than monofilament strings. Monofilament strings are made up of one large fiber that is typically stiffer in nature and more durable.
Within the two broad classes, the types of materials used to make the strings and the string's thickness (gauge) will each play a part in the string's overall longevity. The most durable material is polyester, while natural gut strings are the least durable. A string with a gauge of 15 is considered to be "thick" and will tend to last longer. A string with a gauge of 18 is considered to be "thin" and will not tend to last as long.
Tension maintenance is how well a string retains its original tension once it is installed in the racquet. Different strings lose tensions at different rates (depending on how the string is constructed and with what material). Thus, if a player is using a string that loses tension quicker, the will have to re-string their racquet more often to combat this tension loss.
Care of strings:
By storing your racquet at room temperature and avoiding radical changes in temperature and moisture you will extend the longevity of your strings. In general, you should not leave your racquet in a hot car for an extended period of time or out in the rain. By properly caring for your strings you will not have to re-string as often.