[2021-08-11 15:09:30] [myUsername INFO] 2/7 Try to load profile from 'LittleSkin'.
[2021-08-11 15:09:30] [myUsername DEBUG] Try to request 'https://littlesk.in/csl/myUsername.json'.
[2021-08-11 15:09:40] [myUsername DEBUG] Failed to request https://littlesk.in/csl/myUsername.json (Exception: java.net.SocketTimeoutException: Read timed out)
[2021-08-11 15:09:40] [myUsername INFO] Profile not found.

Already tested on HMCL and PCL2. The JSON skin file exists, but it failed to load.

there have been some issues with https://littlesk.in/csl, try to modify the config file .minecraft/CustomSkinLoader/CustomSkinLoader.json:

{
//...
    "loadlist": [
        //...
        {
                  "name": "LittleSkinCN", // LittleSkin -> LittleSkinCN
                  "type": "CustomSkinAPI",
                  "root": "https://mcskin.littleservice.cn/csl/" // littlesk.in -> mcskin.littleservice.cn
        }
        //...
    ]
//...
}