Emails disappearing after reading

Intego Antivirus - please read the first 600 posting on these Forums and then decide if one what's to keep or remove this unless software.

If removing, do so as per the Developers Specific Instructions.

There are no known Windows-like Viruses in the wild that self replicate and affect macOS, because of the underling UNIX  Foundation and Permission Limitation. 

The The Built in Security  is all that is required to protect the computer.

The only thing this software is protecting is the Bank Account of the Developer and Zero return to the User ( you )

Delete the antivirus first of all, because they don't do any good with your mac. It might be the reason why it's disappearing in the first place. After you do delete it, does the problem continue?

If it still continues, try reading this discussion? https://discussions.apple.com/thread/7620298

If it still doesn't work, try safe mode: How to use safe mode on your Mac - Apple Support

If the Original Installation took place and both Application are appearing in the Applications folder ( you say they are there ) they are running.

Check with the Developer of this Software for Specific Instruction to remove their Software.

Just Drag and Drop to Trash and empty Trash will leave elements of the applications still installed on the computer and may make the bad situation even worse.

Cleaning apps are not good for macOS. They don't do good. You literally don't need cleaning apps. They just make it worse. There was this person who couldn't even upgrade their macOS because of a cleaning app.

You can try "AppCleaner" as a last resort to get rid of the program and its misc. files.

I disagree. I have used AppCleaner for years to remove apps and associated files for an app and as long as the app is not shared with another app by same supplier I have never seen any issue..