Thanks for the tests. As no one had the same result of mine. I'm going to post some screenshots. At the same time, I hope some dev can comment on this.
My experiment was very very simple. I had a linear empire with an equally linear trade route of 8 planets without any stabilizers. As it was an 2v2 AI I was winning a lot, nothing could have interfered and harmed my trade. In fact, nothing flew in or out of my systems with trade except my ally's ships and ,of course, trade ships during my test. I have also only taken the following screenshots only after my rebuit trade station have relaunched all the trade ships and reached maximum income. (The effect of changing length in the longest trade route, however, seems to be instantaneous to other trade stations)
I apologize for the inconenience of having to copy and paste the url into your browser bar. I never posted images on forums before....
So this is what i have , 8 planets with a single trade station on each (7-jumps route)
Note : The ice planet, Calliope, has 30% trade bonus to its own station (nothing to do with the trade route)
[URL=http://img68.imageshack.us/my.php?image=withstabilizersgv8.png]

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Step 1 : scuttled the trade station at the lower left end of the trade route. (terran planet, Lyubov)The result was obvious. One less trade station and a one jump shorter trade route (-0.1cr/s on all remaining trade stations)
[URL=http://img207.imageshack.us/my.php?image=scuttledtradecentreqh9.png]

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Step 2: built a pair of Phase stabilizers at both ends of the original trade route.
on Lyubov (Terran)
[URL=http://img239.imageshack.us/my.php?image=phasegatelyubovgz7.png]

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on Saskie (Volcanic)
[URL=http://img207.imageshack.us/my.php?image=phasegatesaskiewj3.png]

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Step 3: This is where it gets interesting. Rebuilt the trade station on Lyubov.
[URL=http://img245.imageshack.us/my.php?image=withstabilizersmj8.png]

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Now I have a 'longest' trade route of only 4 jumps. 3 jumps less than without the gates, hence, 0.3cr/s less for all trade stations. Why is it so? placing a pair of stabilizers on both end of the linear route is simply like sticking both end of a strip of paper to form a circle. The longest disctance between 2 furthest points on the paper is halved.
This is a very logical result in terms of game mechanics. What the game has done is to pick the longest direct route and treat normal and artificail trade lanes equally.
In a branched empire, the effect may be compensated by taking the trade to another branch. Theoratically, when more phase stabilizers are built, the other branches are also shortened. My experiment was to illustrate that making use of phase gates will result in a trade route that is shorter than the longtest possible route that the natural phase lanes would give.
You see , phase gates are used for connecting the furthest points of your empire to improve mobility. As these furthest points are also where trade routes are based on, shortening them now reduce trade income, which to me, is kind of ridiculous.
Destroying all my trade centres after having built stabilisers on every world (I had 10 planets in the test) then rebuilding them did result in a different trade route - but it was exactly the same number of jumps as before.
The point is, those stabilizers do alter the longest trade route. This means they can reduce the number of jumps of the longest route. Resulting in the exact same number of jumps(hence, income) may simply be coincidental. The logic is that if the phase stabilzers alter trade routes, they will shorten the longest route. If your previously second longest trade route or the new routes created is not as long as the old one, you will recieve less income.
Incidentally, the basic trade income for a trade port (for Vasari, at least) appears to be 1.3 cr/s + 0.1 cr/s for every jump in your longest trade route. Destroying trade ships temporarily lowers the income from a port, until the port automatically builds a replacement.
My results appear to show that the trade income per port is
1.1cr/s + (0.1 * no. of jumps in longest trade route) cr/s