The avatars are cached in eM Client and only update once every 30 days. So if an avatar for a sender was just recently cached, and then they change their Gravatar for example, it will take a while for eM Client to display the new one.
But you can force an immediate recache.
With eM Client closed just delete the avatar folders in C:\Users\yourusername\AppData\Local\eM Client. You may have to enable hidden items in Explorer to get there.
Restart eM Client, and they should start updating.