I've recently been made aware that users in my installation cannot interact with the source code editing in the same way admins can. This is preventing use of iframes (the option in security settings allows them), and extends to users being unable to embed videos using the Insert HTML5 and Insert by link options. Every time they either enter code or embed using those options, then save the question, the code either disappears totally or is stripped back to just a few tags.

Can anyone shed any light on what might be happening? Is the only solution for a superadmin to create questions that need these options?

Do you have the XSS filter disabled in Configuration --> Global settings --> Security?

I have now and that seems to have done it! I thought I had tested it earlier but perhaps I hadn't saved the change properly. Thank you!