Water can leak under a kitchen sink in the case of a cracked pipe, missing valve or loose connection, according to DoItYourself.com. SF Gate also notes that a ring nut under the sink can loosen or form cracks, resulting in a leaky faucet.
The quality of the pipes is also a primary issue. Rusting degrades the integrity of the pipes, along with corrosion, and the age of the plumbing may call for replacement. A burst pipe is another likely culprit, and Emergency Plumber mentions a frozen pipe as the primary cause of major pipe damage. A pipe that is frozen results in too much pressure that builds within the pipes, eventually giving way to internal damage.
2 Plumbers notes that pressure can be a problem within itself. There are times when the water pressure is too high. The material of the pipes can also be a problem since major pressure can break pipes made of soft copper or plastic.
Pipe damage may not be so prominent at first glance. About.com mentions that a small hole can be a source of sink leakage. Other reasons are linked to the drain lines or flex lines. About.com also recommends replacing the cartridge or faucet stem as a possible remedy in fixing leakage under a kitchen sink.