If it is a PVC compression fitting, put a bucket under the p-trap and take the trap off.
Odds are good that you will find one of two things. Either the threads were cross threaded, which will affect the pressure seal around the pipe, or the plastic o-ring was caught in the threads at one point in time and was mangled. A mangled o-ring won't provide a satisfactory seal.
Either way you will know which part to replace, and these connections (provided it is compression fitting PVC) can be replaced easily at your local hardware store.
If it seems that everything is fine, look for the following items:
Is the pipe being unnaturally flexed or bent due to particular pipes being too long or short? If so the solution is shorter / longer pipes, but make sure you don't dramatically change the geometry of your setup.
Are the locking nuts really tightened appropriately? Sometimes a good "extra twist" solves a leak in the best possible way. Remember, if you "break" an obviously replaceable section of pipe, you're out a few dollars in plastic, so don't be shy.
The joint between the end of the p-trap and the pipe from the wall is supposed to be constantly under water, so it is fairly common for those to leak. Normally they are fitted and tested for leaks. The workman will not leave with one leaking. Since it is under the sink, and people often store items under their sink, eventually the pipe gets bumped. That's probably the source of your new dripping; however, it is highly unlikely that anyone will remember bumping the pipe, even if they did it.