I think it depends on which bank you are with. HSBC shut my account when I was selling BTC and only reopened it on the understanding that I would not do any more BTC trades on the account. I think the red flags were receiving lots of bank transfers from individuals and receiving a transfer from someone on a watch list of suspicious accounts or something.
HSBC lol.... not like they do anything illegal.
http://www.bbc.co.uk/news/business-18880269