We've come across an intermittent issue with our CRM users (2013 SP1). The issue is describes in this article -

https://crmtipoftheday.com/670/if-activities-disappear-take-this-pill/

We run Outlook 2013 (option 2), and tried option 3......to no avail. Option 1 is our next try, but not sure how practical that will be. I've included a screen shot below of what the ACTIVITIES screen looks like after the message is sent (it is empty).