The arrangement you describe is entirely symmetrical between A and B so the elapsed time for an orbit will be the same for each satellite.

Your question about how can both clocks be running slower than the other is based on a common misconception about the nature of time dilation. Time dilation is another entirely symmetrical effect in SR and results from the fact that two reference frames moving relative to each other have tilted planes of constant time. A level plane of time in one frame corresponds to a sloping slice through time in the other, the slope being upwards in the direction of motion. This means that if you synchronise your watch at t'=t=0 with a passing clock in the other frame, at that instant, when it is t'=0 everywhere in your frame, it is already later than t=0 everywhere ahead of you, the value of t increasing with distance.

Consider some point ahead of you where t' is already equal to 1s at the moment in your frame when you synchronise your watch at t=t'=0. If you then take 4s to reach that point, and the clock there also advances 4s while you are completing your journey to it, you will find that it reads 5s when you get there, not because it ticks faster than your watch, but because it was already showing 1s when you started your journey.

  This is a key point to remember about time dilation if you want to avoid various logical conflicts based on misconceptions. It arises not because one clock runs slower than another, but because a moving clock is compared against successive clocks in the other frame which all tick at the same rate as the moving clock but are progressively out of synch with the time in the frame of the moving clock.

The example you gave is based on a misconception that each clock runs more slowly than the other, which is logically impossible. The fact that the satellites are constantly accelerating makes the set-up more complicated and therefore easier to misunderstand, but you can reduce it to a thought experiment in which runners run in opposite directions around a square, and if you like you can replace the square with a hexagon and then with an octagon and so on until you end up with a circle- the physics always remains the same.

And in response to some of the other comments, the arrangement you describe is in principle no different to a version of the twin paradox in which both twins travel out and back in opposite directions and have aged the same amount when they re-meet, in spite of the fact that each has constantly been time dilated in the frame of the other throughout the journey.

The arrangement you describe is entirely symmetrical between A and B so the elapsed time for an orbit will be the same for each satellite.

Your question about how can both clocks be running slower than the other is based on a common misconception about the nature of time dilation. Time dilation is another entirely symmetrical effect in SR and results from the fact that two reference frames moving relative to each other have tilted planes of constant time. A level plane of time in one frame corresponds to a sloping slice through time in the other, the slope being upwards in the direction of motion. This means that if you synchronise your watch at t'=t=0 with a passing clock in the other frame, at that instant, when it is t'=0 everywhere in your frame, it is already later than t=0 everywhere ahead of you, the value of t increasing with distance.

Imagine you are travelling at set your watch at t=0, and at some point ahead of you there is a person whose watch is set 1s ahead of yours. If you then take 100s to reach that person, you will find that their watch reads 101s when you get there, not because it ticks faster than your watch, but because it was already showing 1s when you started your journey. That is broadly analogous to the way in which time dilation rises in SR. It is not because moving clocks slow down, but that the path they take through spacetime has a shorter elapsed time which they correctly measure as being less. This is a key point to remember about time dilation if you want to avoid various logical conflicts based on misconceptions. It arises not because one clock runs slower than another, but because a moving clock is compared against successive clocks in the other frame which are progressively out of synch with the time in the frame of the moving clock.

The example you gave is based on a misconception that each clock runs more slowly than the other, which is logically impossible. The fact that the satellites are constantly accelerating makes the set-up more complicated and therefore easier to misunderstand, but you can reduce it to a thought experiment in which runners run in opposite directions around a square, and if you like you can replace the square with a hexagon and then with an octagon and so on until you end up with a circle- the physics always remains the same.

And in response to some of the other comments, the arrangement you describe is in principle no different to a version of the twin paradox in which both twins travel out and back in opposite directions and have aged the same amount when they re-meet, in spite of the fact that each has constantly been time dilated in the frame of the other throughout the journey.