Stellarium 0.10.4: planet orbits change over time?
Probably this is due to the fact that orbits of the Earth and Mars are inclined to the ecliptic differently so our viewing angle of the orbit of Mars changes slightly over the year.  The program is probably showing the orbit of Mars projected onto the Celestial Plane as seen by us on the one specific date. Note, this is different from the ephemeris orbital data which gives the apparent position as seen by us at each date/time.   Just a guess though.