Hi Pete,
I wonder if your peat pots are moist enough to encourage the roots to continue growing through them. I know that if you leave the peat pots of young garden plants above soil level, the pot will act as a wick to the surface and the plant's moisture will be drawn out. The young plant can wilt or die because the roots won't be able to penetrate that dry pot--even though it's in the ground. Because of that, I always tear the top of the peat pot down to below soil level before I plant my seedlings in the ground (prevents wicking). Also, you'll see that most of the peat pots at the nursery have a cut-away plastic covering on the pot that prevents moisture loss through it. The plastic will bend down over the top edge of the pot toward the plant's roots to prevent wicking from the pot's top edge. These will usually have root growth through the pot, no problem.
Because of the wicking effect, I prefer just to use plastic cups for my plants (no peat pots). If I read your post right, you already have the peat pot in a cup. I would cut/tear a couple of those pots back to an inch or so below the level of the soil. You will then have to add soil (to keep the top edge of the peat pot covered), then water and see if that improves the roots growth.
Good luck,
Mimi