Hi kazuhart
If you're continuously being prompted to reset your password, it sounds like you're changing the password for the wrong EA account- please look over the Connected Accounts section on your EA account, if you're not seeing your Steam account linked there, that's one way to verify you're using the wrong login details.
You'll need to locate the EA account your Steam is linked with and update the password for that account- if you need more help locating the correct login details for your account, that's something the live support team can help with here.