DIAGNOSIS This is a classic sign of a worn drive link tang (the part of the chain that fits into the bar groove) or, more commonly, a worn bar. As the bar groove widens from use, it can't hold the chain tightly.
FIX First, inspect the bar, especially the groove the chain runs in. Look for a "hooked" or widened opening. If it's visibly worn, the bar needs replacement. If the bar looks okay, the issue is likely your tightening procedure. Here's the right way: 1) Loosen the bar nuts. 2) Lift the tip of the bar up to take slack out of the chain. 3) While holding the bar tip up, tighten the bar nuts firmly. The chain should be snug but still pull freely around the bar by hand.
IF THAT DIDN'T WORK The chain itself might be stretched beyond its service life. Chains do stretch, and a severely stretched chain won't hold tension. Compare it to a new chain. If it's significantly longer, it's time for a new chain.
HEADS UP Overtightening is a common mistake and can damage the bar, chain, or even the saw's motor bearings. A properly tensioned chain will have a little bit of sag on the bottom side of the bar, but should not droop away from the bar. Always re-check tension after the first minute of use on a new or cold chain, as it will seat itself.