There are these types of people talked about by Jesus in His parables.
As for what was sown on rocky ground, this is the one who hears the word and immediately receives it with joy, yet he has no root in himself, but endures for a while, and when tribulation or persecution arises on account of the word, immediately he falls away.
Matt 13:20-21
They hear the word and receive it with joy, notice the high emotional state, endure for a while, then fall away when things get hard. This is exactly what you are describing. Jesus says they do this because they have no root in themselves.
What is this root? Jesus tells us in Revelation 22:16, "I am the root". He says they have no root, then calls Himself the root. In other words, they fall away because they don't have Jesus in themselves.
They weren't truly born again to begin with, despite their high emotional state at the time, because it isn't a matter of emotion.