Avot337

8:
Our mishnah teaches that the sin of Jeroboam, in which he facilitated idolatry, is so great that he could not be given the opportunity to repent. However, it is almost axiomatic in the Jewish religion that "nothing can stand in the way of repentance". He who is truly and sincerely penitent will be forgiven the most heinous of sins. Rambam [Repentance 3:14] writes:

This, of course, prompts the question: why could Jeroboam not repent?

9:
Rambam wrestles with this seeming contradiction later on in his clarification of the laws of repentance. And the result of his wrestling has very important ramifications for most painful theological problems in our own day and age. (See my essay on Theodicy.)

10:
Perhaps we should first note the rather strange language of our mishnah. Why does our mishnah say that Jeroboam was not given the opportunity to repent? Surely, if "nothing stands in the way of repentance" nothing could prevent him from contrition if he had wanted to show contrition. Rambam relates to this problem in connection with a different, but similar, instance. Several times in the account of Moses' confrontation with the Pharaoh we are told not only that Pharaoh hardened his heart [Exodus 8:11, for example], but also that God hardened Pharaoh's heart [Exodus 10:1, for example]. How are we to explain this egregious interference with Pharaoh's free will? Without absolute freedom of choice there can be no such thing as good or bad behaviour, no possibility of moral choice. If God can control our choices we can hardly be held responsible for the consequences of those choices, our actions. And if we cannot be held responsible for our actions there can be no such thing as sin and wrongdoing.

11:
Rambam explains [Repentance 6:3] that there must be occasions when the sin is so heinous that the very idea of repentance is abhorrent. In such cases God actively prevents repentance so that the culprit will inevitably get his just deserts. Pharaoh ordered the elimination of half the Jewish people [Exodus 1:23]. Any concept of moral justice cannot conceive that such a crime could go unpunished, could be forgiven. Pharaoh is, of course, a long way from our minds. So in my essay on Theodicy I offered a different example:

In the essay, of course, I expand on these ideas greatly, but there is no room for such expansion here.

12:
The sin of idolatry is the very antithesis of Judaism's core teaching, the existence and unity of the deity. The sin of one who facilitates idolatry from the public can therefore not be permitted to be expunged by repentance. It is for that reason that Jeroboam (and his likes) cannot "be given the opportunity to repent".