In the film, we learn that the date is sometime after July 1998 but before December 1999. That date appears on Neo's Security file and Morpheus specifically references "*the world as it was **at the end of the Twentieth Century***" in his '[desert of the real][1]' speech.

I think we can be reasonably certain that your **hypothesis 1** is the closest; 

 - Time in The Matrix advances normally until it reaches late 1999.
 - The inhabitants are then memory-wiped and reset to an earlier date, say January 1st 1990.
 - Repeat ad infinitum

This loop has presumably happened at least 40 times since creation of The Matrix, factoring in the time between the end of the Machine War, the creation of the [Paradise Matrix][2] and the [Nightmare Matrix][3] and the present day.

![Security Record][4]


  [1]: http://youtu.be/tgBViHeiSKM?t=50s
  [2]: http://matrix.wikia.com/wiki/Matrix_betas
  [3]: http://matrix.wikia.com/wiki/Matrix_betas
  [4]: https://i.sstatic.net/Saum1.png