Problem:
Outlook is unable to download new messages, and deleting emails from your inbox produces errors.
The Outlook desktop application produces the error:
Outlook.ost data file has reached its maximum size. " Cannot postpone the reminder. The outlook.ost data file has reached the maximum size. To reduce the amount of data in this file, permanently delete some items that you no longer need.
Cause:
Outlook desktop application local data is stored in the Outlook.ost data file. This error indicates that your email profile contains too many emails or too many attachments, making it too large. 
Solution:
Since your email is stored in the Microsoft Exchange cloud, the solution is to reduce how much Outlook keeps on your computer.
Step 1: Empty Deleted Items and Junk
- In Outlook, right-click Deleted Items → Empty Folder
- Do the same for Junk Email
Step 2: Delete or Move Large Emails
- In Inbox and Sent Items, sort by Size
- Delete old or unnecessarily large messages (especially those with big attachments)
- If you need to keep attachments:
- Save them to your U:\ or OneDrive
- Remove them from the email.
- Remember to empty the deleted items
Step 3: Adjust Cached Mail
- Go to File → Account Settings → Account Settings
- Select your email account → Change
- Under Mail to keep offline, move the slider to keep fewer months (e.g., 6 months instead of All)
- Don’t worry — older mail stays in the cloud and is searchable in Outlook Web (https://outlook.office.com/mail/).
- Do this for each email account you've added to Outlook
Step 4: Restart Outlook
- Close and reopen Outlook.