Game time calendar
--
Our group solves the exact problem you are describing using a game time calendar. This is essentially exactly what it sounds like: a table listing dates in a column, with checkboxes next to them on which we can mark the passing of days. We also left some space for short notes.

We used this extensively in a very long sandboxs like fantasy campain (set in Middle Earth with MERP/RM). It helped us keep track of the day-to-day events, as well as regular events like income, arrival of trading companies, shipments, due taxes, etc.

*Example (too lazy to look up the proper Arda month names ;) ):*

 +-------------+---+-----------------------+
 | Date | ? | Notes |
 +-------------+---+-----------------------+
 | January 1st | X | Left the city |
 | January 2nd | X | |
 | January 3rd | X | Ran into some orks |
 | January 4th | X | Hunted down ork chief |
 | January 5th | | |
 | January 6th | | |
 | January 7th | | |
 | January 8th | | |
 | .. | | |
 +-------------+---+-----------------------+

Advantages:

* Quick to use: a simple check mark is mostly enough.
* Notes allow for a coarse log of what happened in an efficient way
* You can easily annotate important dates in the future (How long until the smith finished the sword for player X? When is the next paycheck comming in?)
* With proper formatting you can easily fit half a year on an A4 sheet.

In your case you might have to keep this calendar to yourself (as GM) if you intend to note down things like "Arrival of the evil lords armies". Otherwise I suggest just outsourcing this: give it to your most meticulous player and let him do the bookkeeping for you.