At this point in that video, some minutes after the loss of signal, you can hear on the countdown net https://youtu.be/-B_tWbjFIGI?t=42m21s - it's garbled but sounds like "Suspected loss of signal".

But they also say the insertion was successful. So the payload made it, but they were planning to recover the center and that failed?

Correct. There were several goals with the launch. The primary was successful payload insertion, the secondary goals were the successful return of the outer two boosters to land, and the central booster to a drone ship down range (success unknown). Additionally the goal was to recover the fairings, but the success of that is not publicly known at this time.

According to News Conference: 1) Elon confirmed that the faring recovery was not a goal as they have a new version of the faring in active development which should have a recovery strategy in place. 2) It appears that the center booster was definitely lost. 3) Loss of center booster was best case scenario for loosing one of the three boosters as the outer boosters had really sweet new titanium grid fins.