What is the ruling on one who vows to perform the night vigil (qiyam al-layl) and to remember Allah constantly without stopping, and is it possible to reconcile this vow with the demands of daily life such as work and social interaction?

If the vow is conditional on a specific action (a vow of 'lajaj' - obstinacy/anger), one can either fulfill it or offer an expiation for breaking an oath (kaffarat yamin (definition)). However, if the vow is a vow of 'tabarrur' (seeking nearness to Allah), such as making it conditional on receiving a blessing, then it is obligatory to fulfill it, and it is not permissible to resort to expiation unless there is complete inability. As for continuous remembrance (dhikr) without interruption, this is impossible for humans; therefore, it is necessary to maintain dhikr outside of times of necessity, and no expiation is required in this case.