Is it obligatory to continue performing two rak'ahs of gratitude after every obligatory prayer throughout one's life, knowing that one does not perform the Sunnah prayers?

If you verbalized what you intended with your tongue and meant it as a vow (nadhr), then you are obliged to perform two rak'ahs after every obligatory prayer that is followed by a supererogatory (nafila) prayer. However, if you did not verbalize it, and it was merely an inner thought or an intention without the purpose of a vow, then nothing is obligatory upon you. Nevertheless, it is recommended for you to maintain it as an act of obedience.