I am having the same issue. I have had my phone for about a week and the time was correct until this past weekend.
I selected New York as another city and it showed the correct time, but the weather info for NYdoes me no good.
Indiana was until a few years ago was on Standard Time, but we have switched to Daylight Savings Time. I noticed that Microsoft and other OS manufactures still list Indiana as a separate time zone. I am sure the problem is some time zone offset in an XML file, but that does not explain why the time was correct for the first week.