"When I click on a meme and hit the upvote button, It doesn't stay lit when I go back to the stream I was scrolling. Does this mean the upvote goes away? "
Hit F5 or refresh the page when you go back to the stream, your upvote should be visible there.
"...or will it be cancelled if I re-click the button from the stream? "
If you upvoted on the image page and then went back to the stream and upvoted again to make it green there, there is no cancellation or duplication. If the upvote is green on the image page or in the stream and you click the button again, you will take away your upvote.
You can always verify whether your upvote has registered on an image page by checking here:
imgflip.com/my-upvotes