I also had this problem the other night and lost all my .sync folders as well. Strangely not all my devices were affected. In case it provides clues as to what went wrong, here is the sequence of events as I remember them. Everything had been working fine for a few months since I installed BTSync and bought a Pro(Business) license.
1. I was doing some filesystem housekeeping between my MacBook Pro and iMac both running the latest El Capitan 10.11.5. I was deleting files from my Documents folder and actually enjoying the speed of syncing between the devices as they were next to each other and I could see one update the other.
2. After 10 mins or so I noticed that the Sync program on my MacBook Pro was showing that everything was disconnected. At this stage the iMac was still looking normal. My first thought was that I had lost WiFi connectivity or Internet connectivity but I quickly discounted that possibility. Then my iMac Sync program went the same way and everything became disconnected.
3. I checked my iPad Sync program and it appeared to be working fine and was still connected although I'm not sure if maybe some of the selective sync folders maybe changed to disconnected. I can't quite remember how I had it set up.
4. I checked my iPhone 6 Sync program and it was completely disconnected from everything.
5. Finally I checked my Mac Mini server which is running in the MacMiniColo data centre in Las Vegas and runs encrypted folders which mirror my local folders for data backup and security reasons. This machine runs the free version of Sync because I don't want it to have anything but encrypted folders on it for security reasons.
I did some googling looking for s Sync status page to see if this was a known issue but found nothing. I then found this forum thread but couldn't register an account to make a reply because the Captcha widget was complaining the domain was wrong. I then manually hooked up all my connections again but had to go through a very unnerving "indexing" phase where all my machines tried to decide which machine had the latest files. This took overnight and well into the next day to complete and I'm now sitting down to try and figure out if any of my files got lost or damaged. I hope that the sync algorithms you use are sound and this shouldn't be a problem but I've got to tell you, this was a very very unnerving episode and greatly reduces my faith in BitTorrent Sync. I moved from a Drobo FileTransporter to BTSync because it had a great reputation for speed and reliability and that has been my experience until this happened. I hope that you can find the cause quickly and give reassurance that it won't happen again.
btw, my Macs were all running 2.3.6 although I updated the iMac to 2.3.7 to see if that would help reconnect (it didn't). I was afraid to do anything to my Mac Mini in the data centre in case it also disconnected everything before I had a chance to resync all my machines. I'll probably go ahead now and update all the machines to the latest software but I see from others above that this probably won't help avoid the problem.
Good luck fixing this, if I can be of assistance then please let me know as I am a professional developer and have a lot of experience of sysadmin as well so can easily extract any logs and other data that you might need.
Many thanks,
Craig.