I apologise in advance for providing a complex technical answer to your question, but in this case you most likely have a complex technical problem.
Your problems are possibly due to a Javascript conflict with either your current WordPress theme or one of the other plugins you are using - see Contact Form 7 Email Issues - there is a link there that covers Javascript Conflicts.
on_sent_ok is the generally the absolutely last thing that runs in CF7 so any interferring Javascript Conflict can stop this running.
Step by step approach to finding JavaScript Conflicts
1. Switch temporarily to a WordPress default theme (Twenty Eleven etc.) and see if the problem goes away.
If it does, you’ve most likely got a JavaScript conflict with your current WordPress theme.
If switching to default theme doesn’t help it could be one of the plugins you are using that is causing the problem.
2. Disable all plugins other than Contact Form 7
If doing that solves the problem, you can then add back each item – one by one, until you find the real cause of the problem.
You will need to disable, temporarily, ALL JavaScript, other than that from CF7, including anything in your theme (switch temporarily to a default theme), if you want to get to the source of the problem.