I have had this problem, currently only managed to get 3 pea plants, I just have to cover everything, seed trays with lids are good, I also have a propagator (not plugged in) in the greenhouse which they cant get into. Lots of people here seem to be saying once they're bigger they are ok, but I just had my only two mange tout plants which were at least 15cm tall, pulled out of their pot, snapped off from the root! They were fine when in smaller pots on table but I had re potted them and had the pot on the floor of greenhouse. Im wondering if this is more likely to be a rat? We are on a smallholding so they are around, not sure how it is getting in though! Very upsetting as they were doing so well! Think Im just going to grow them in the house for a while!