Hi,
What type of email account are you using? Exchange, IMAP or POP3? If you are using an Exchange account, this issue would happen if you only have two weeks of emails cached to local. To verify this, go to File > Account Settings > Account Settings,
double click your email account to open the Change Account Wizard. Make sure the "Mail to keep offline" slider is not set to 2 weeks.

This issue could also happen if you have AutoArchive enabled for Inbox, which will delete old emails or move them to the local archive folder. To verify this, right click your Inbox, select
Properties and click AutoArchive tab. Make sure the 'Do not archive items in this folder' option is currently selected.

In addition, do you have any custom view/filter applied to your Inbox? Your emails could be hidden by these views/filters. We can try to start Outlook with
/cleanviews command to reset all custom views to default to fix the issue. To do this, exit Outlook, press Windows key + R to open the Run command, type
outlook /cleanviews and press Enter.
Hope this helps.
Regards,
Steve Fan
Please remember to mark the replies as answers if they helped.
If you have feedback for TechNet Subscriber Support, contact
tnmff@microsoft.com.