We have been having this issue for months too. I am on this forum researching it for our finance manager who wants to get from QBO because he has simply had enough. It creates hours more work a month for him than he needs to do. I am technician and understand the issue. It is a complete moving target trying to maintain mail servers reputation in a world with so much anti-spam protection. Something mass mails many thousands, or even millions, messages with links and attachments is going to be tricky to keep from being blocked. 

What I don't understand is why QBO do not offer the option to relay your outbound email to your OWN mail servers and manage your reputation yourself. I could solve this problem for us TODAY if they included it, like many cloud providers do. Simply enter your smtp mail relay server and QBO hands off to that server for email delivery - it worked for QB Desktop. This approach also allows you to deliver emails from your own domain name and with branding, to personalise the experience. Not a free 'advert' for QBO - not that it is doing them any favours at the moment. 

Come one, Intuit - add an outbound mail handler (MTA) and let us get back on with running our businesses!!!