Hello marietc, So you are using an ISP's email service. If your email ends @btinternet.com, @btopenworld.com or @talk21.com it's a BT email
I went to the site and they are making email changes. Have you seen this page from their site?
https://www.bt.com/help/email/manage-email-account/updates
You may want to contact this company and ask them about your Flagged emails disappearing. Or according to the site you can also use these email clients; Apple Mail , Outlook, Thunderbird, Windows Live Mail.
Unless you really like their service I would switch to Apple Mail since you are using an iPhone, but that is just my opinion. Sorry I can't offer more help.