Answered by Shaykh Amjad Rasheed
What are the characteristics of the socks which makes wiping over them permissible? What do I do if I have been wiping over my socks (thin and thick ones) for years?

Just like the khuff, socks must fulfill five conditions before it is permissible to wipe over them during wudu. They are:
1) That they be strong such that one can walk continuously on them for the length of time that a traveller would in his comings and goings to fulfill his needs, such as going somewhere to fulfil his needs, such as relieving himself, buying food, and so forth. It is not intended that one must be able to walk in them throughout the duration of the journey.
2) That they be thick, whereby if water is poured on it, it would not penetrate through quickly.
3) That it completely cover the part that is to be washed during wudu, which is the feet including the ankles.
4) That they be pure of filth
5) That they be worn after one has made a complete wudu, having washed both feet first, for if one washes one foot and puts on one sock, then washed the other foot and puts on the other sock, it is not permissible to wipe over them.
So whenever a sock fulfills these five conditions, it is permissible to wipe over it, and when it doesn’t, then it is not valid. It follows from this that anyone who [s. in wudu] has wiped over their thin socks or socks that aren’t strong enough, his prayers are invalid in our school, so he must make them up. This is the same in the Hanafi and Maliki schools, because their relied-upon books verify the invalidity of wiping over thin socks.
As for the Hanbali school, some ascribe to it that it is permissible to wipe over thin socks. When glancing at their books, it seems that sometimes, it is mentioned as permissible and sometimes it is not, and I am not certain regarding their relied-upon position. However, the erudite scholar, al-Mubarkafuri, said in his commentary of “Sunan al-Tirmidhi”, that the Hanbali madhhab agrees with the majority on the position that wiping over thin socks is not permissible.
In any case, the established position in the three schools is the invalidity of the prayer if one wiped over their thin socks during wudu, as most socks are these days, and he must make up those prayers. However, what seems to be apparent to this impoverished soul, is that it is not obligatory to making up these prayers immediately because of the large number of people these days who give fatwas that it is permissible [h. to wipe over thin socks] because of which [h. wiping over thin socks] has become widespread among the non-scholars to the extent that they denounce that fact that it is not permissible (which is the sound position). This [h. widespread] dubious position is sufficient [as excuse] from people having to make up the prayers immediately, because they did not [h. perform an invalid prayer] through open violation. And Allah knows the truth best and to Him is the return and the final abode. – Amjad Rasheed
(Translated by Sr. Shazia Ahmad)