Mysterious pea problem

Hello, I wonder if I can pick your brains about my peas. I have grown them in a couple of different gardens over the last few years without any bother. I tend to sow them in batches in modules in the greenhouse and plant them out in succession.
Last spring I planted out a couple of trays of healthy (about 6-8 inch) plants and I usually put in a few seeds at the same time for insurance. The plants seemed healthy enough but didn't grow at all for a couple of weeks and then slowly disappeared. I tried a couple of further showings in different areas of the veg plot and the same thing happened. This year the exact same thing has happened again!
I know pigeons and slugs will make short work of the young leaves and that mice can dig up the seeds but could it be that there might be something in the soill which is checking growth first before the slugs and birds then take advantage. The plants were hardened off and didn't seem to be frost damaged.
Any ideas?
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In my experience, mice or voles will take the whole young plant. I have had entire trays of three inch high sweet peas taken. they were in the greenhouse. A mousetrap sorted the problem.
Thanks for the reply. i agree that mice are one of the suspects I would like to "bring in for questioning". I put wire mesh over the trays when they are germinating which seems to work but it seems to be that it is once they are in the ground that something is going for them. I am going to give it one last try (this year) with planting out a last batch. I think I will add a bit of mulch too. Any other suggestions?