When you exit and reload the game, any characters in your profile that are based on classic skins from a Marketplace or custom skin pack are deleted. This doesn't happen for characters imported from a skin file.

Note: In my own testing on Windows 10, skins from Marketplace packs work correctly, but there are additional reports saying Marketplace skin packs have the same problem..

I have attached a sample skin pack that can be used to reproduce the issue.

Steps to reproduce:

1. Download the attached skin pack and double-click to install it in Minecraft.
2. On the main menu, select Profile.
3. Select any character, then click Edit Character.
4. Select the Classic Skins (2nd) tab.
5. Expand the Owned section. It should contain the Sample Skin Pack.
6. Choose any skin from the Sample Skin Pack.
7. Back out to the main menu. The selected skin should appear as your current skin.
8. Exit Minecraft and restart it.

Expected results:
Your current skin is the one you selected from the Sample Skin Pack.

Actual results:
Your current skin has been replaced with one of the defaults (Steve or Alex). If you open the Profile, the skin you selected is no longer saved in any character slot. The skin pack is still available on the Classic Skins tab, however.