In the Logs I see for every broken transcode similar entries.
Plex seeks for a segment which is not available.
Using ATV4 with tvOS 10.2.1
Plex App is 1.12 (5992)
Plex Server is 1.7.5.4035
Jul 06, 2017 20:12:36.284 [0xea335b40] VERBOSE - * Accept-Encoding =>
Jul 06, 2017 20:12:36.284 [0xea335b40] VERBOSE - * X-Plex-Http-Pipeline => disable
Jul 06, 2017 20:12:36.284 [0xea335b40] VERBOSE - * X-Plex-Device-Name => Wohnzimmer
Jul 06, 2017 20:12:36.285 [0xea335b40] DEBUG - Asked for segment 425 from session.
Jul 06, 2017 20:12:36.285 [0xea335b40] DEBUG - We're in a seek: asked for 425, min/max available was 400/420
Jul 06, 2017 20:12:36.285 [0xea335b40] DEBUG - Segment #425 WON.
Jul 06, 2017 20:12:36.285 [0xea335b40] DEBUG - Killing job.
Jul 06, 2017 20:12:36.285 [0xea335b40] DEBUG - Signalling job ID 7579 with 9
Jul 06, 2017 20:12:36.286 [0xea335b40] DEBUG - Job was already killed, not killing again.
Jul 06, 2017 20:12:36.286 [0xea335b40] DEBUG - Stopping transcode session 2C374581-297E-4F0A-AFFE-FDFD3C3BBBF6