If the time for wiping over the socks ends or he takes off his shoes, is his wudu invalidated?

Firstly: 

If the time  for wiping over the khufoof has ended, and you have wudu, then your wudu does not become invalidated, according to the correct view, which was favoured by a number of scholars, including Ibn Hazm and Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on them), because there is no evidence that it becomes invalidated. Wudu is only invalidated by the well known causes such as passing wind. See question no. 69829. 

Based on this, if the period (for wiping over the socks) ends whilst you are praying, then you should carry on with your prayer, and pray as much as you want so long as you do not break your wudu. 

Secondly: 

If a person takes off the khufoof or socks after wiping over them, his wudu does not become invalidated according to the correct scholarly opinion. That is because when a man wipes over his khufoof, he has completed his purification according to the shar’i evidence, and when he takes them off, this purification remains in effect, based on shar’i evidence, and it cannot be rendered invalid except with shar’i evidence. There is no evidence that taking off khufoof or socks that have been wiped over invalidates wudu. Based on this, his wudu remains in effect. This is the view favoured by Shaykh al-Islam Ibn Taymiyah and a number of other scholars. See: Majmoo’ Fataawa Shaykh al-Islam Ibn Taymiyah (21/179, 215) and Majmoo’ Fataawa wa Rasaa’il al-Shaykh Ibn ‘Uthaymeen (11/179). 

But taking off the khufoof brings the period for wiping over them to an end, i.e., he cannot put them on again and wipe over them, until after he does a complete wudu in which he washes his feet. 

And Allah knows best.