Triac's gate isn't fully activated
Most likely you have insufficient current flowing through the LED to keep the triac on. The current required to keep the TRIAC on is called the holding current. Unfortunately the parts datasheet doesn't list a minimum, but it's clear you are below the value.

If you look at the datasheet for a FKP12N80, you will see that the holding current is 50 mA. Your part's holding current is most likely very close to this value.