Update to Twonky Server 8.2.1.
Yes, I was having the same problem with Twonky Server 8.2 simply quitting after 30-45 minutes. I'm running the latest Mac OS 10.11.3.
I therefore did what I always do...Look for an update! I found the latest version is 8.2.1 so I updated and it now seems to be working much better. It also seemed to rescan much faster.
Since I'm new to using Twonky, I'm a little shocked that there is no auto update or even "update available" warning anywhere to be found. I believe, especially with problems like this (unusable software!) that it is important.
I'd also like to add to make sure you select "Improve My Experience" in your Advanced settings. This is probably how their programmers figured this out. E-mail support is so old school so I went straight to the forums for the answer (that I gave).