I've been having the same problem today! And I'm really worried.
This has only started happening today whenver I open the app "Whale Trail". Earlier, I had purchased (using real money) something from the app for the game, and ever since then, whenever I opened the app it asks for my apple id password. If I click cancel it works just fine, but it asked me that every time, so I just ended up putting in my password. It stopped asking for my password after that, but then a while later once I opened up the game again, it asked for my password again!
So in total I've put in my password 3 times. I'm worried that it's charging money into my account whenever I do that! However, I checked my account, and it doesn't say that it's charged (It usually says how much money is charged right after I use the card). So for now, the amount charged on my account is still the same as earlier, so it looks as if no money has been charged, but I'm still worried! On the game, it didn't add anymore points to the points I have (which means that I didn't buy the points) and on my account it doesn't say that any extra money is charged. So hopefully, it didn't accidentally charge my accoutn 3 more times! Especially since it didn't even give me the extra points for the game! So it would be charging my account for nothing.
Anyways, I ended up taking off all billing info on my account (other than my address and stuff), so it won't be able to charge it to my account or my card.
It only happens with this one game, and it only happened after I purchased the extra points, do you think it's charging my account several times for the points? Because if it is I'm not even getting the extra points! So I don't think it is, and it doesn't say anything on my billing statement online either. I'm just worried.
And like many users above, if I click the cancel button on the request the app works fine.