This will occur if the page already has a Membership Form or Event Registration Form in place. Only one can be present on a page at at time. This may also happen if the part is added to the template and you try to insert a duplicate onto the page.

If you don't see the part initially, while editing the page, check the following areas:

Page
  1. Navigate to Site Explorer>Pages & Templates
  2. Click the Search tab
  3. Search for the name of the page you're trying to insert the part on
  4. Once you find the correct page, click on it in the upper pane to highlight it
  5. In the lower pane, confirm if the membership form or event registration form part type exists
    • If a part is here, you will not be able to insert a duplicate
    • If you see a part here, but you don't see it while Editing the page, click the Scissors icon to cut the part, then insert the part back onto the page.
Template
  1. Navigate to the page you want to insert the part onto
  2. Click Edit this page
  3. Click the Template Designer Button
  4. Do you see a part listed here? 
    • If a part is here, you will not be able to insert a duplicate
    • If you don't see a part here, make note of the template name:
      1.  Navigate to Site Explorer>Pages & Templates
      2. Click the Search tab
      3. Search for the Template name
      4. Once you find the correct template, click on it in the upper pane to highlight it
      5. In the lower pane, confirm if the membership form or event registration form part type exists
      6. Click the Scissors icon to cut the part, then insert the part back onto the page
Note: If you would like to add more than one event to a page, you can edit the Event Registration form and add another event.  This process is outlined in the Event form section of the Parts Guide.

Corrupt Page
Note: If the event registration form part is grayed out, but there are no other event form parts on the page or template, then the page may have become corrupt. One scenario in which they may happen is if the part lived on Template A and Template A was associated with the page. The page was updated to use Template B, which doesn't have the same content pane as Template A, so the part is hidden. 
You may change the template of the page until you find the template which allows the part to be seen, and then cut the part off. Alternatively, you may go ahead and create a new page for the part to be placed on. You cannot copy the page, as it will copy whatever is corrupting the page.