You're rendering a tab that does belong in profile edit in profile edit. This is why you're having issues. You've a FORM element within a FORM element and that's not valid HTML which breaks the save. Specifically you're rendering the Profile Update Log in profile edit. Do not do this. If a tab doesn't have a profile edit display it does not belong there.
I've unpublished your cb_profile_update_log field and confirmed profile edit save works fine again. If you need to view a users update log in backend then I suggest using the profile update log page in backend specifically for that. If you want a field that sends you to the log you can pre-filter the page via a link to it. Example as follows.
index.php?option=com_comprofiler&view=editPlugin&action=showpulog&cid=PLUGIN_ID&pulogbrowser[filter_user]=[user_id]
Replace PLUGIN_ID with the plugin id of the CB Profile Update Logger plugin. In your case you'd use the following.
index.php?option=com_comprofiler&view=editPlugin&action=showpulog&cid=544&pulogbrowser[filter_user]=[user_id]
You can now just put this in some HTML to link to that users update log and it will pre-filter the backend view to that user. Example as follows.
Code:
<a href="index.php?option=com_comprofiler&view=editPlugin&action=showpulog&cid=544&pulogbrowser[filter_user]=[user_id]">Update Log</a>