Good question.
Not really easy to answer.
The main problem is that there is no guidance in the legislation and there is virtually no case law to create a clear definition. This means we can only guess. However from trial and error, it's safe to say that the critical word here is exceptional.
This means, not your average day, 'forgot the card on the kitchen table' or 'forgot to top up the balance because I'm a bit vague' or 'I slept in and was going to miss my bus/tram/train if I validated my card' sort of circumstances.
It means something has gone seriously...EXCEPTIONALLY amiss and it really seriously affected your ability to have a valid ticket.
It could be a temporary super bad day kind of circumstance - for example your myki had expired and you had no chance between realising and meeting the Authorised Officers to replace it . Or it could be a problem caused by being very new to Melbourne public transport or having very limited English language.
Now, before you start dreaming up the worst day ever...you will need some evidence of extreme events, so if you had your wallet stolen, for example - you could be excused for travelling home without a ticket, but you will need to get a police report to attach as evidence.
If you were very ill, or a relative is in hospital, or anything serious that might have contributed to you not holding a valid ticket, you should try to get some documentation of this - such as a medical certificate or hospital record.
It also means that there may be ongoing situations where you simply couldn't afford to top up your myki or where things were going so badly for you that topping up your myki was pretty much bottom of this list.
Some examples might be:
Other chronic exceptional circumstances would be debilitating life events such as serious acute illness, language or literacy difficulties and cultural differences. So being too sick to keep up with whether your myki has a positive balance, or being unable to understand how the Melbourne Public Transport system operates because you have just arrived in the country would be examples of these circumstances.
In any event - you can see that 'exceptional circumstances' need to be...well..exceptional. Don't bother saying that you just forgot or it was an accident - that won't work.
To make your case more compelling, it is important to provide evidence or some sort of proof of your claim. For example, medical or hospital records or a letter from your doctor, a copy of a death certificate, a police report, a letter from the bank about your cancelled bank cards.
Got it?