As you may be already aware, you have been able to manage authentication session (aka control the frequency at which your users need to re-enter their credentials) with SharePoint Online for quite some time by using the Azure AD Conditional Access.
Well, now you can do the same for Exchange Online. You can use the same authentication session policy you set for SharePoint Online or create a new one.
From there create a new policy (or edit the existing one for SharePoint Online)
Configure as your desire for the Users and Groups, Cloud Apps (if you want to have a different one for ExO and SPO) and then configure the ‘important’ section Sessions by setting up the Sign-in frequency option and/or the Persistent browser session
- Sign-in frequency controls how often users get prompted to sign in. Sign-in frequency can be set from 1 hour to 365 days
- Persistent browser session controls when users can remain signed in after closing . The two settings are “always persist”, or “never persist”
In both cases, your users will no longer see the “Stay signed in?” prompt.