DIAGNOSIS The tactile membrane switch behind the power button is failing or has poor contact. This is a known weak point on some units.
FIX This requires a precise press. Use the pad of your finger, not the tip. Press firmly and deliberately in the exact center of the button. Hold for a full second. The inconsistent response is due to a worn internal contact pad.
IF THAT DIDN'T WORK Consider using the monitor's auto-wake feature. Leave the monitor powered on at the wall outlet. Set your PC to turn the monitor on/off via the DisplayPort or HDMI signal. You'll rarely need to touch the physical button.
HEADS UP Do not repeatedly mash the button. This can worsen the internal contact damage. If it fails completely, the repair involves disassembling the monitor and is not user-serviceable.