Attributed to Ignatius Brianchaninov
«"He who is careless about prayer is careless about his salvation; he who quits prayer renounces his salvation."»
Misattributed
Verdict
It is not in Ignatius Brianchaninov's work
It circulates in English under his name (the English Wikipedia quotes it) without reference to a specific work; it has not been located in the chapters on prayer of the Ascetic Experiences consulted. It is consistent with his teaching, but the exact wording remains to be verified.
What they did say
Verified words of Ignatius Brianchaninov
«Delusion is the damaging of human nature by falsehood. Delusion is the state of all human beings without exception, produced by the fall of our forefathers. We are all in delusion. Knowing this is the greatest protection against delusion. The greatest delusion is to consider oneself free from delusion.»
«О молитве Иисусовой», Отдел II, «О прелести» (Аскетические опыты, t. I, cap. 27).
«It is natural for beggars to beg, and for man, impoverished by the Fall, to pray.»
«О молитве. Статья I» (Аскетические опыты, t. I, cap. 12), primera frase.
«The way to God is prayer. The measure of the way travelled is the various states of prayer into which one who prays rightly and constantly gradually enters.»
«О молитве. Статья I» (Аскетические опыты, t. I, cap. 12).