Ok found it.
Using the credit card account
(3) How you can use the credit card account
(a) The credit card account must be used wholly and exclusively for your personal, domestic or household use
Unfortunately that seems to be pretty clear cut.
Many people do of course put through business spend on private cards, but in your case they have examined the spend.
The interesting part of this is who has the onus of proof. Does the bank have the onus of proving that it was business expenditure, or is it the card holder who has to prove that it wasn't business expenditure / it was all personal?
If the first one, then raising a complaint to the ombudsman would be interesting as it would rely on the bank coming with a strong case. I suppose they will start by saying that the cash amounts being put through the card represent an extremely unlikely case of personal expenditure, though that - in and of itself - isn't sufficient proof. The pattern of merchant names might suggest something that the bank used as its basis for terminating the OP's account.
Of course, one might adopt the view that the bank can do whatever it wants in its reasonable determination, as its rules allow it to do. To what extent they can exercise their "free wielding" discretion may be a point of contention in law, but then you'd have to find under what legal grounds has the bank overstepped the mark.
Reminds me of the bloke who churned his NAB credit card with 1c transactions before the bank caught up with him. Lucky for him, NAB simply told him that he wouldn't get diddly for any transactions after they caught on, but as for those which he already got points for, they let him have them. Probably more difficult for NAB in this case because it was a Qantas credit card, viz. direct sweep, which means any points already swept to Qantas are very difficult for the bank to claw back.
And here's an interesting AusBT article from a few years ago:
The world's five weirdest tricks to earn frequent flyer points - Australian Business Traveller