Problem

After I reply to an email message in Gmail, it is removed from my Inbox.

Solution

When replying to an email, you will see two buttons at the bottom of the message.  Both buttons send the message but the blue one also "archives" it, removing it from the Inbox.

If you would like to disable the "Send and Archive" button:

1. Go to Gmail
2. Click the gear icon in the top-right corner
3. Select Settings
4. Under Send and Archive, select Hide "Send & Archive" button in reply