For giggles I ran the maths on station VEL13:10:8, on cyclers it might run from Venus, to Earth, and to Mars.
Laplacians didn't bother with cyclers in the Jovian planets, and the same seems to hold here. Venus to this station (approximating nine Venus years to two synods, but I suppose I could try 13-to-1) incurred a nasty offset of 13.49° on return; and there just weren't cyclers from the station to Earth (five orbits to one synod). Permacyclers tend to assume higher-order resonances between planets, like Earth:Mars; even Venus:Earth was a bit of a stretch.
The station kind of is a cycler, being the Venus-Earth Hohmann without the "transfer" part. Everything here is one-way; if someone is stuck here, s/he's there until the next Hohmann window out.
So: how's the cycling from the station to Mars?
I got 7 interior orbits to 4 synods. 2.04° internal offset is twice Earth-Mars-Earth's but arguably not so bad with a shorter orbital circle. Problem here was the angle: the Aldrin alone has insane angles to both planets and is a fryby in order to get to Mars in the first place. Four synods does offer wiggle-room for permacycles but it turned out, not enough.
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