I did some research on the matter because why not, and I found some interesting information.
It could be for multiple reasons, such as your antivirus blocking the download of some files - specifically McAfee and PremierOpinion (in which case you need to visit the Mojang Support Center here:
http://help.mojang.com/customer/por...e-can-i-find-more-help-and-technical-support- and disable them to fix it) or for way simpler reasons.
Try switching to different versions of Minecraft, especially vanilla versions (1.9 for example works just fine for me) - although I doubt this could really be the issue.
You could also try stopping your Minecraft game session, delete the contents of the skin folders
.minecraft/assets/skins/ and restart your Minecraft.
If any of those shouldn’t work, try contacting Mojang support for bugs specifically. All the information I’ve gathered can be found here:
https://bugs.mojang.com/browse/MC-101579 (just so you know I’m not trying to mess with your computer lol). However, I think the very first option should be the one that can fix your issue.