That's not the reason Jesus said they "fell away" nor does He say they ever had the truth in the first place. In fact, they never understood the word. Yes, they "fell away" during a time of testing, BUT, He doesn't say it was "because" the times of testing proved to hard, that they fell away. People assume that, contrary to the Text.
Mark 12:24 Jesus said to them, “Is this not the reason you are mistaken, that you do not understand the Scriptures or the power of God?
Is it necessary that someone understand the Scriptures and the power of God in order to not hold mistaken beliefs??? Yes!
Matthew 13:20-21 (ESV) 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.
Did the rock have any root in himself??? No!
Matthew 13:23 (ESV) As for what was sown on good soil, this is the one who hears the word and understands it. He indeed bears fruit and yields, in one case a hundredfold, in another sixty, and in another thirty.”
Did the rock understand the word??? No! The good soil was the one that understood the word.
Matthew 13:13 (ESV) For this reason I speak to them in parables, because seeing they do not see, and hearing they do not hear, nor do they understand,
The rocky soil:
1. didn't understand the word,
2. had no root
3. held mistaken belief
For these reasons, they immediately fall away.
Only soil that is rooted in the Root and thus understands the power of God, proves to be His. The rest, hear something they just don't understand and hold mistaken beliefs.