Apparent gaps will be magically healed as Mail app caches the entire Inbox.
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Sometimes, it takes a bit for an email to come through on your i Phone via the Mail app.
You can in fact access the more recent items (via your web mail or even an alternate email app or email client.) The Mail app is actually grabbing the wrong subset of your Inbox email which causes some email to appear to be missing.
The Mail app is showing you the emails that got moved into your Inbox most "recently" instead of your "newest" emails.
Newer versions of Mail app automatically retrieve the next series of email from your server each time you hit the bottom.