Am I required to offer expiation or make up for the votive prayers that I did not perform, which are estimated at approximately one hundred rak'ahs?

Undertaking a vow is disliked (makrooh), but a conditional vow must be fulfilled if the condition is met. So, if you said, "I vow to pray two or three rak'ahs if such and such happens," then if it does not happen, nothing is required of you. But if it does happen, you are obligated to perform the prayer you vowed, and this obligation is not waived by the passage of time; rather, you must hasten to fulfill it. You should be cautious regarding the number of prayers you vowed if you are unsure of the exact count. Expiation (kaffarah) for a vow is only permissible in cases of continuous inability that is not expected to cease. You can perform these prayers gradually.