But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea, which is moved and carried about by the wind. Therefore let not that man think that he shall receive any thing of the Lord. A double minded man is inconstant in all his ways James 1:6-8
Inconstancy denotes withdrawal from a definite good purpose. Now the origin of this withdrawal is in the appetite, for a man does not withdraw from a previous good purpose, except on account of something being inordinately pleasing to him: nor is this withdrawal completed except through a defect of reason, which is deceived in rejecting what before it had rightly accepted. Thomas Aquinas, Summa, ii-ii, q. 53, a. 5
This image of Inconstancy beautifully portrays the one that is "moved and carried about the wind." She is completely unbalanced. It makes me a bit queasy to look at her. The garment around her waist is blown up into the air. She perches precariously on some sort of wheel and even the floor beneath her is rolling like a wave of the sea.
I'm wondering if that wheel represents the Wheel of Fortune, that medieval concept in which Fortune blindly spins her wheel, and he that is king today becomes a slave tomorrow, and vice versa.
The faith of the inconstant man reels under the vicissitudes of life. When things are going well, he makes resolutions and keeps them, but when troubles come he loses his balance, his resolution fails.
As you can see, I had a very difficult time finding any references to inconstancy. There were plenty of passages that used the word as an adjective, but nothing much that described what inconstancy is. The only exception is the above answer to a question in the Summa where Thomas argues that Inconstancy is not a vice that opposes Fortitude, (as in this series from Giotto) but one which opposes Prudence.