If Fast Secure Contact Form uses no Javascript that could resolve a Javascript conflict.
Remember that a problem in one script can cause issues in another. For example, some jQuery errors can stop jQuery processing any more script, which can make the culprit hard to find. A jQuery error in one of your plugins or your themes javascript files can stop jQuery processing before it gets to the CF7 script.
If this resolves your question, it helps others contributing here, if you can flag your post as [resolved]