Your logs are showing that you system isn’t using hardware encoding but instead falling back to software encoding.
2017-10-02T22:38:52 MCEBuddy.AppWrapper.Handbrake → [22:38:52] qsv_enc_init: using ‘software’ implementation, API: 1.23
2017-10-02T22:38:56 MCEBuddy.AppWrapper.Handbrake → Encoding: task 1 of 1, 0.13 %
2017-10-02T22:38:58 MCEBuddy.AppWrapper.Handbrake → Encoding: task 1 of 1, 0.17 %
2017-10-02T22:39:00 MCEBuddy.AppWrapper.Handbrake → Encoding: task 1 of 1, 0.20 % (7.26 fps, avg 13.90 fps, ETA 00h44m30s)
This would indicate an issue with your graphics drivers or hardware. Try using a different driver, maybe the latest Microsoft WHQL driver or the the latest one from Intel’s website. You’ll have to try different versions until you find out that works.
Maybe also try this version of Handbrake and see if makes a difference.
https://handbrake.fr/rotation.php?file=HandBrakeCLI-1.0.7-win-x86_64.zip
Your other logs shows that the encoder is failing due to a corrupted video:
2017-10-02T21:06:59 MCEBuddy.AppWrapper.Handbrake → Encoding: task 1 of 1, 2.57 % (8.27 fps, avg 8.83 fps, ETA 01h08m25s)[mp4 @ 0000000006af0f00] pts < dts in stream 0
2017-10-02T21:06:59 MCEBuddy.AppWrapper.Handbrake → ERROR: avformatMux: track 0, av_interleaved_write_frame failed with error ‘Error number -22 occurred’
Are you facing this problem just a single video or all video files?