The ansvr installer puts a shortcut to start ansvr in your Start menu Startup folder, so the first thing to do is to check the Startup folder in the Start menu to confirm that the shortcut is still present. If the shortcut is not there it means that something removed it. Anti-virus program perhaps?
If the shortcurt is present, but you cannot access the ansvr settings (the message about site refused to connect when you go to http://127.0.0.1:8080/api/config), then it means that something caused ansvr to stop. If that is the case, please post your ansvr log so we can see what happened. The ansvr log file is C:\Users\YOUR_USERNAME\AppData\Local\cygwin_ansvr\var\tmp\platesolve\ansvr_DATE-TIME.log