This is a frequently asked question (FAQ) that many people using Microsoft Outlook as their email client found their meeting invitations automatically deleted and moved from Inbox to Deleted Items folder once they've clicked on the button to accept or decline the meeting invitation.
The accepted meetings will appear inside your Calendar.
I believe many people prefer to keep the original meeting invitation emails inside their Inbox instead of deleting them, because the invitation email might contain important information about the meeting, such as the meeting agenda, attached documents, etc.
In fact, deleting responded meeting invitations from Inbox is not a bug, but rather a strange default behaviour of MS Outlook.
To change that default setting to retain your meeting invitation emails inside Inbox, go to File > Options, the Outlook Options dialog box as below will popup.
Select Mail on the left menu, scroll down to the Send messages section, and uncheck the option of "Delete meeting requests and notifications from Inbox after responding".
Click the OK button and you are done.