In your screenshot of the controls, it does not show you matching on your login controls. Specifically, form1 is not matching. Is that just a bad screenshot, or does it not match? If it isn't matching, you'll need to resolve that.
As for saving credentials, there are several ways. The easiest is to use the ASO Manager.
I tried to delete and re-assign all my controls. Then I found out that when I interrogated the web first time, green checks will appear besides “frmlogin”, “btnSign_In”,”txtpwd”, “txtUserID” icons. But when I click “Stop Interrogation”, and start again, these green checks will disappear.
Does that mean they are not matched? If so, how can I resolve that?
Yes, that means they are not matched. You'll need to look at the match rules for frmLogin as it must have a match rule that does not work every time the page loads. Perhaps it is using a URL match rule and the URL changes. You'll need to establish what is different between each launch to correct that.