I was checking the fourth era lore on UESP and can't find the mention of when the Isle of Artaeum disappeared along with the Order. Can anyone remember? Could they have been somehow responsible?

- I should specify the second disappearance, not the first where the Isle of Artaeum reappeared 500 years later.

Heh, were they were researching what caused the disappearance of the dwemer ..... and found it?

My understanding is that the island disappeared only once, but when it returned 500 years later, the Iachesis (Rite Master) and the original Council of the Psijics did not return.

The second "disappearance" is not so much a physical disappearance but rather a diminished presence in Tamrelic affairs. According to the fragment, http://www.imperial-library.info/content/fragment-artaeum, emperors, Uriel VI, Morihatha, Pelagius IV, and Uriel VII, have been suspicious of the Psijics enough to refuse ambassadors from the Isle of Artaeum within the Imperial City. This is probably due to an unsubstantiated legend that accuses the Psijics of creating a "freak storm" that helped King Antiocus defeat King Orghum. Even discounting the truth of the legend, the Psijics that reappeared seem to be even more secretive and monastic than they were before.

Here are some sources that may be of help:

http://www.imperial-library.info/content/guide-psijic-order
http://www.uesp.net/wiki/Lore:Psijic_Order
http://www.imperial-library.info/content/fragment-artaeum