[EDIT] After discussing this with Jeff, I've come to a different view on events. My original stance was that there is only one timeline and John was always fighting with the same "version" of Skynet. Jeff says:
Aaron, there can't be only one timeline. That's the whole point, as made clear in the second movie.
He refers to the "NO FATE" carving which led Sarah on her crusade to kill the engineer who build the first T-800.
In this light, the events play out like this:
Timeline 1: Skynet is built with the normal technology that we know today. The resistance struggles and eventually overcomes all of Skynet's defenses. Skynet was calculating this as the likely result and built a time machine to save a different version of itself in a different timeline. In the nick of time, Skynet 1 sends the first T-800 (T-800-1) back into the past of Skynet**-2** (timeline 2).
Resistance sends Reese-1 back into timeline 2 as well.
Note: In timeline 1, Reese-1 can't be the father of Conner-1 - nothing was sent back into timeline 1 from any other timeline. This timeline is basically the start of the whole war.
Also note that the first movie starts with timeline 2. Timeline 1 is only visible in Reese's flashbacks.
Timeline 2 starts to split itself from timeline 1 when the T-800-1 arrives. This is a new timeline and events unfold differently. In this version, Skynet-2 is much stronger to begin with since it has the design of the T-800-1 to build upon.
But Skynet-2 is not yet strong enough. Skynet-2 also sees that it will eventually be overcome but it has better technology and maybe already knows that a time machine is possible. So Skynet-2 sends T-1000-2 back to try again while the resistance sends T-800-2 back (each side goes up one notch in available technology). In "R
Skynet-3/Conner-3 meet the new T-1000-2/T-800-2 and Skynet-2 gets his circuits kicked in by Conner-2.
Timeline 3: Conner-3 and T-800-2 fight with T-1000-2. This leads to Skynet-3 who builds T-800-3 (who manages to kill Conner-3) and T-X-3.
Timeline 4: T-800-3 helps to save Conner-4 and his wife. Skynet-4 learns how to merge Terminator technology and humans. No terminators are sent back in the movie
but of course, this Conner must have met a version of T-800-1 and T-800-2.
It's important to note that the timelines split when a machine arrives from the future. This means that Conner-1 never meets any terminators before Skynet becomes conscious. Conner-2 meets one T-800 (T-800-1), Conner-3 meets two, etc.
Also, upto the moment the machines arrive, Conner-(x-1) and Conner-x are the same person. If that were not the case, we would need many future timelines to provide for all the terminators in the past.
To repeat Conner-3 has met T-800-1 (tried to kill his mother) and T-1000-2 but those two were sent back by different versions of Skynet from different future timelines. Conner-4 has met the same T-800-1 as Conner-2 and Conner-3 but each of their timelines split as soon as they met someone from the future (one version didn't meet anyone from the future - this isn't visible in the movies - and the other version follows a new timeline).
You could also interpret this differently: "Something about the field generated by a living organism."
Maybe Reese was referring to the fact that the time machine was a living organism that would not send a pure machine back. For him, this could have been obvious but in the nick of time, everyone else misinterpreted his words.
On top of that, Reese is a soldier and he probably doesn't know much about how the machine works - maybe he's just repeating something that the scientists were mumbling as they tried to understand how to make the thing work (note that they probably knew what it was because John Conner knew because of Reese).
Or more likely, the script writer needed a reason that sounded at least slightly plausible ;-)
Lastly, some time passed between the first and the second attack through time. Maybe Skynet was able to improve the design.
But that doesn't explain why the first T-800 didn't come with a huge arsenal of weapons to level the playing field.
There are a lot of holes here:
In the first movie, Skynet is defeated, so who sent the second terminator back? Where did the second machine come from? How and when did Skynet send the T1000 and the TX back? Or did some subsidary of Skynet re-conquer the original machine?
Obviously, no RPG players were present when this was designed. As Skynet, I'd have skinned a couple of humans and wrapped my original T800 in the (dying but still living) tissue covering some really nasty gear. To gory? Well, why didn't Skynet simply put guns and ammunition under the skin of the T800? It doesn't feel pain. It would have looked a bit bulky but only for a few moments until the trip is over.
One possible explanation is that Skynet feared that the advanced technology could fall into the hands of the resistance but then, it knew in detail what had happened in the past (it had access to the whole story by accessing the various government computers when it came alive - maybe it became so hostile because it read there that it would ...). That would mean it didn't send the technology back because it hadn't done it or because there was really a risk that we don't know about.
So IMO, the most likely explanation is: Because there wouldn't have been a sequel otherwise. It's a glitch.