Fathers of the Desert story A Catholic friend of mine told me of a story from the Fathers of the Desert.

The story goes that one of the followers of the desert monasticism would sneak off at night seeking sin; but he would confess his sin to God each night on his return; because of this the brethren could not "see" his sin.  But one night whilst this chappy went on his "rounds" and upon returning he was tempted of the Devil that his sins could not be forgiven this time, and he believed it; because of this the brethren immediately could "see" the student's sin.

My question is as follows: Does anyone know of this account and where I might find a full account of this story in a book or some online resource?
I don't recall this story, but that doesn't mean anything.

The full text of the alphabetical collection of the Sayings of the Desert Fathers appears to be available here.  As far as I can tell, it is a verbatim version of the Cistercian Publications 1975 edition (at least the Indices seem to match).

The Evergetinos is an arrangement of teachings on various subjects from various sources, including the Desert Fathers, arranged by subjects ("hypotheses").  The first "hypothesis" seems to relate to your question:  "No one should despair ever, even if he has committed many sins, but should have hope that, through repentance, he shall be saved".  There are 6 stories from the Desert Fathers in this section:  one from Abba Mios, three from Abba Poimen, one from Abba Sisoes, and one anonymous.  But none of these are your story.  Will be interested to see if someone finds a better answer.