As I was grown up in Hiroshima,
I'm native to Hiroshima dialect which is known for its rough and provoking wording.
Let me add explanations about practical use of じゃけぇ/じゃけん(both are totally same) among Hiroshimans on Mr. electeur's answer.
じゃけぇ is composed of two particles:
assertive particle じゃ+ conjunction けぇ.
Its composition is same as だから.
However in Hiroshima dialect, we use じゃけぇ/じゃけん in many situations.
Eng 'We better root more cuz Carp is behind'
In this usage, じゃけぇ is same as だから.
I have to note that じゃけぇ and だから is used when speaker want to stress the conditional clause.
So じゃorだ is not necessary if the speaker doesn't care much about Carp's being behind.
- Assertive particle
Eng 'I am a Carp fan.' or 'I'm crazy about Carp.'
Note: Carp fans are famous/notorious for its crazy enthusiasm towards the team.
Eng 'Hey!(Oi!) what the f are you doing?'
Depending on speakers' tone, this じゃけぇ is often regarded as an offensive interjection.
Above 3 usages of じゃけぇ are often heard in Hiroshima dialect.
Let's move on to the sentence in the question.
'知らんがー 落ちたモンは 落ちたんじゃけぇ'
As for the state verb '知らんがー', in the actual plot, he is asked why he failed.
Thus '知らんがー' must connote anger or bad temper.
Translation would be ' I don't f care!' in the context.
As for '落ちたモンは 落ちたんじゃけぇ' part,
I assume this じゃけぇ is simply an assertive particle like above example 2.
落ちる means fail. Thats correct.
So I would like to translate the sentence.
'I don't f care! Fail is a fail.'