The soil looks quite dark, have you perhaps over watered?

I have a row of sweet peas, planted in the ground some of them are like yours and some are doing really well although no flowers yet. So I would be interested to know as well sorry I have not been much help.

It's too cold, when it is like this the plants take up a limited amount of moisture, so do not need watering as much, particularly if in a container.

It can be the same outdoors if the weather is cool and wet!

I wish someone would tell mother nature to stop watering my plants as much and get her to warm things up a bit ;o))....Tg

Groan, yes, we need some warmth and sunlight, anyone'd think its March, not June. Agree with Teegee's comments.

Probably lacking nutrients and need planting out.

I agree with Teegee - cold winds have done this to mine in the past.

The main problem is that people are starting their sweet peas off too late. To have any chance of overcoming our barmy climate, plants need to be grown much earlier and planted out much earlier.
Mine at the moment are 3/4 foot high and looking very healthy, but that is because they were started off in December and planted out the end of March/early April.
Having said that, I'm having my worst year ever for bud drop, and that is entirely due to the cold damp conditions.
I am hoping we get a bit of sunshine soon so that they can grow through this in time for the National show which is just 5 weeks away. Otherwise, i'll be exhibiting some rather nice stems but no flowers :)

From looking at your pictures, my gut feeling is that your bottom 6 plants won't recover, but the top 6 if planted out ASAP will be OK.

As an aside, if those Cells are part of a 15 or 24 cell insert tray then really they aren't big enough for sweet peas . Five grown in a 6" pot is the ideal.

Whenever I planted mine out early the same thing happened to them, every time. I reckon three of the bottom ones actually stand a good chance of recovering if there are no more setbacks - really hope so anyway.