You will need to examine the guttering lengthwise first to ensure that it is sloping correctly. The slope should be toward the corner and at least 1/4 inch, but no more than 1/2 inch for every 10 feet of guttering. If the slope is less than 1/4 inch, that may be the cause of your issue. Rainwater, snow and ice can easily weigh down improperly sloped guttering, causing enough pressure to eventually separate the corner joints. You can fix this by removing and reinstalling the guttering with the appropriate slope. Clean and fully dry the area. Place a thick layer of sealant on the area and reattach it. Once it's reattached, apply a generous portion of sealant over the top of the seam.
Failure to clean your gutters can result in a situation similar to that in Section 1. When massive leaf piles clog up your guttering, they can become remarkably heavy when wet. Over time, all that weight can cause separation at the corner. If this has occurred, clean out your guttering, ensure that the slope is correct and clean and thoroughly dry the area. Repeat the sealant procedure described in Section 1.
Weather and time can do a number on the caulk used to seal the joints of your gutters. If the caulk has become brittle and cracked or has withered away, this is likely the cause of your gutter corners leaking. To remedy this, take a scrub brush and clean this area of the gutter with soap and water. Make sure you rinse any soap away prior to drying the area. Soap residue can prevent the caulk from adhering properly when you reseal the joints.
Metal can become damaged over time because of corrosion from standing water and rotting leaves. If you have multiple types of metal used in your guttering, then dielectric corrosion may be the culprit. You may choose to repair the corners of corroded metal guttering, but you will eventually have to replace it.
There are several different brands of sealant available, but each manufacturer has a suggested brand for a reason. The sealant chosen usually depends upon what materials the guttering is made of or coated with. If you are uncertain which manufacturer created your gutters, end caps are noted for being stamped with the name of the manufacturer.