I recently spoke with someone who works as a compliance officer at a large bank (in the US) regarding this issue. She basically told me that accounts that move a lot of money in and out of the country automatically trigger alerts that put them into the so called high-risk category. These accounts then need to be kept under closer tabs, as in someone needs to manually track subsequent suspicious transactions and either file Suspicious Activity Reports or record down the reasons why the bank thinks that the transactions are not suspicious after all. (This could be as simple as someone from the bank calling you and asking you what these wire transfers are all about and then adding your response to the file.) Failure to do so could result in heavy fines against the bank. This is a lot of work for the bank, so at some point the bank just closes these troublesome accounts if they feel that the revenues that these accounts bring in do not justify the costs required to maintain regulatory compliance.
This is true for both personal and business accounts, but the handling of each is different.
Why couldn't they just ask the customer to stop the undesired transactions rather the closing the account preemptively?
A) An individual account, if you're an ordinary person, isn't too important to them. In aggregate, they are, yes, but any single account, not so much.... much easier just to have a form letter go out and be done with it.
B) The bank is operating under the assumption that whatever activity that's going on in the account is activity that the account owner needs to do. So they'll say "well, when we opened the account, he was just a regular depositor like all the others, but now he's doing all these international wires and shifting money all over the place, we don't like that". They don't look at transactions as being optional (they'll never say "would you please stop depositing money into your account?" or "if you wouldn't mind, please stop making withdrawals" (second part, actually, they will for savings accounts and money market accounts; those account types are limited to 6 withdrawals or less per month otherwise they convert to checking accounts. Not like there's any difference in this day and age of 0% interest rates, but when that changes, there MIGHT become more of a difference between checking and savings)