why do my old e-mails disappear from Cloud?

Hello Unhappywoman,

Thanks for using the Apple Support Communities!

From your post, I understand that old emails are being deleted after a month. This could be due to the mailbox behaviors set for your iCloud account.

The following article explains how look at these settings. My suspicion is that the section “Permanently erase deleted messages when:” is set to One month old.

Use Mail Preferences to set or change options for the email accounts you use in Mail, and for working with messages and mailboxes. Choose Mail > Preferences, then click a preference pane to view options:

Accounts: Add, delete, and disable your email accounts in Mail. Use the Mailbox Behaviors pane to control how draft, sent, junk, and deleted (or “trash”) messages are stored. The Advanced pane includes options for messages, attachments, and more.

Set Mail preferences - Mail Help

Cheers!

You could try Rebuild of your Inbox. Go into your Inbox then click Mailbox / Rebuild (bottom of selection list). This will rebuild your Inbox and retrieve Inbox mail from the server. You may have to select another mailbox (e.g. Sent) then your Inbox to start seeing emails being retrieved.

Also, if you have an iPhone or iPad using the same email account, make sure you're not deleting email from those devices as that will affect the same account on your Mac.