Time passes normally inside the Matrix. Technology and society is kept at the same level (approximately 1999) by aggressive Agent tactics. The Matrix has never been reset.

Argument

It's generally assumed that the date remains roughly around 1999, resetting periodically. There is basically two ways to allow for the date to stay the same: Mind Control and Alternate Time Frame. We can largely dismiss the latter. The events of the movie inside and out match. The only sources of dilated time are in the comic books which we do not consider canonical (and even if you did, they are always special cases involving a single individual).

That leaves Mind Control. The belief they can completely change individual minds is very dangerous because Neo's interview should have gone differently... rather than trying to intimidate him into co-operation, they should have simply reprogrammed him: "You are completely loyal to us- an agent of the Agents- and will do whatever it takes to bring us Morpheous. Maintain your cover as the hacker Neo, join his crew, then betray them from the inside." or something like that. A "hypnotic suggestion" could be built into all humans that should they ever see a pod or wake up, the Agent mentality will take over. Basically, we dislike the idea that minds can be reprogrammed.

If we take away those two means, how else can the Matrix be restarted, or for that matter even be started? The theory of time passage is tied closely to how the Matrix is initialized. Please go read that first.

There are some older dates referenced in Neo's file going as far back as his birth. We believe that the system started with date like 1850 but with 1999-approximate technology and that the Matrix (other than initialization) has never been reset. Human society has largely been stagnant for 100 years. How can this be maintained? Agents acting like the Men in Black, basically. Consider how technological breakthrough and information are disemenated... it's done electronically or through the media. As long as you control those, you control the flow of information and thus belief.

The only plot hole with this is that they have pre-1999 contemporary elements (like "The Prisoner" or the Lincoln Continental) that are diverse then suddenly a stagnation of society... but would the average person think about that if they didn't read it in the paper? And what if your history books were filled with sociological theories on how humanity had reached Equilibrium (a naturalistic/evolutionary-type theory easily swallowed by minds presented with no other alternatives).

Why then is it 1999 just when Smith talks about 1999? My personal feeling is that the Oracle had a hand in creating the Matrix and picked the initial date with The One in mind... a bit of irony on her part. But theoretically, under this model, if The One didn't come along, the Matrix could go on for another few hundred years (the date always moving forward) to say 2299 and still be at 2000-approx society/technology/etc. level.