I've got three padron peppers on the go, all in the exact same conditions, but one of them keeps getting a wobbly stem. The other two have strong firm stems and stand upright, but since about three days ago this one has taken to leaning over and being really bendy. I thought maybe it was thirsty, so gave it a drink, and it perked up and the stem was firmer, and then the next day it was bendy again. The soil looks really moist in all three pots, so I don't know why this one plant is being odd. It looks healthy otherwise and the leaves aren't affected, though it is less vigorous than its peers, since it doesn't have any sideshoots yet.
All three are in 5" pots in the greenhouse in multi-purpose compost. No sign of flowers yet.