Generally speaking, there should be no difference in altitude loss between a downwind turn and an upwind turn, but the wind velocity versus altitude gradient at only a few feet altitude can cause some interesting effects. For example, as soon as you bank into a turn while flying upwind, the low wing will be flying in lower velocity air, causing it to lose lift and, if it is anywhere near stall, also develop more drag, since its true angle of attack will also be higher than that of the high wing. This will tend cause the low wing to drop further, steepening the bank angle, resulting in the nose dropping. This is the only reason I can see for the widely held belief that downwind turns result in dramatically more altitude loss than do upwind turns.

Years ago, when I flew freeflight quite a bit, I noticed that a model that was trimmed for slow circling would tend to fly straight downwind after it reached a sufficiently low altitude at close to stall airspeed. I think that the reason for this might be if the model tries to turn a bit, the low wing will be at a slightly higher airspeed, since the wind velocity will become lower as the ground approaches. Let's say that the model is flying at an airspeed of 15 MPH with a 15 MPH tailwind, with a 30 MPH groundspeed. If a wing dips a sufficiently to get into 14 MPH wind, that wing will have an airspeed of 16 MPH, tending to increase its lift and causing it to raise slightly. The high wing may, similarly, be in 14 MPH wind, tending it to lose lift, and lower slightly. The reality is probably far more complicated, what with the effect of ground-induced turbulence burbles and all.