Why do my emails disappear sometimes?
It isn't in the nature of email itself for emails to go missing.

This means that mails go missing either because:

(a) someone is accessing your account and deleting the mail,

(b) there's a server problem where data is lost,

or

(c) software has been setup to intentionally delete emails

You indicate that you're using Gmail, but also Mail.app on iOS and Mac. If you store your email on Gmail exclusively, it doesn't sound likely that (b) happens several times for you.

If your account is secure and you haven't shared your password with anyone else, I don't think the problem is related to (a) either.

So the most likely culprit is reason (c). This could be a spam filter, antivirus/antimalware software, etc. that is setup to identify and delete suspicious emails. As you're using multiple clients to access mail, this could have been setup directly on Gmail, in Mail.app on your Mac or on an iOS client.