That's very interesting - I've not seen that issue in the past, and have delivered the time sheet service a number of times. My first guess would be that the time cards are attempting to update the cost plans of projects that span through fiscal periods that have been updated using the old (now legacy) portfolio workbench, and have had the 'open' field updated from true to false.
Are you using the portfolio workbench to track your open and closed fiscal periods? If so, I suggest you have a look at the business driver for this, and evaluate the Strategic Planning Workspace (Portfolio Planning if you're an SPM Std customer). When updated and configured, this will now give you financial and planning information, as well as a huge range of additional functionality.
If you're not using the Portfolio Workbench, head over to the 'Fiscal Periods' module, and make sure you've got the 'Open' field on the list view. Look for any set to 'false' in the affected instance. Most instances don't use that field now, but if you're updating them for any reason, that may be the cause of your issue.
