You cosset your seedlings or buy young plants and expect every one to perform perfectly. This doesn't happen in the real world: plants produce thousands of seeds and only a few make it. So, to beat the natural process, you must take special care of seedlings. After sowing more than you'll need, plant out the best and carefully monitor their progress. You can improve the odds by growing F1s, plants specially bred to produce uniform results for one season.
Transplants face several hazards - different soil structure, temperature and watering regime; damaging winds; and potentially lethal attacks from pests and diseases. You should marvel at the winners rather than bemoan the losers.
When planting out brassicas, celery, lettuce, broad beans and anything other than root crops and peas, the biggest challenge is not damaging the fragile roots. Seedlings are accustomed to fine, uniform compost so they need well-worked, level and stone-free soil. After digging a hole, remove the watering can rose, water into the hole, plant and gently tamp down the soil.
Brassicas and lettuce from a garden centre have often been multiple sown, with several seeds to each plug. Check that the plants are green and healthy, and not spindly with yellow leaves. Plants that are "checked" have stayed too long in a seed tray or plug and have used up all the available nutrients; they'll never recover. You may manage to separate seedlings in a plug, but their roots are often intertwined. Soak the plug and, holding the base of the stems, very gently pull or tease the plants apart. Discard poor specimens. It's much better, if expensive, to snip off all but the strongest young plant.
Root crops - carrots, white turnips, radishes, beetroot - are best sown directly into finely prepared, unfertilised ground as roots are often damaged when transplanted.
Peas can be sown directly too, but I prefer to sow in sections of old gutters no longer than 60-75cm. Once the seedlings are 5cm tall, draw out a broad drill, water it and slip the peas off the gutter. The gutters should be short. You can easily slide two short sections into the drill; longer sections tend to concertina and you end up with damaged roots. Then push in a line of small twigs along the outer sides of the drill for support and protection against crows that would pull out and discard the precious seedlings in their quest for grubs underneath. Regular watering is critical. Root systems lie close to the surface, which readily dries out, so keep watering. Give the plants a good soak once a week, rather than a sprinkle every day. I run a leaky hose along the rows. Admittedly it's easy for me: I divert my overflow into a bin and use a garden hose to feed the leaky hose. A water butt would be just as effective.
With tiny roots, transplants are vulnerable to wind damage and aren't yet anchored firmly enough to resist being buffeted around. Small sticks prevent this and I find yogurt and cream pots do the job for broccoli and lettuces. After removing the bottom of the pot, I twist it into the soil to create a snug microclimate which allows for strong growth. The pot protects against cabbage root fly, which would lay eggs close to the stem of brassicas. Once hatched, the grubs devour the roots with fatal consequences. A circle of Vaseline round the pot wards off any foraging slugs or snails. I leave this guard round my cabbages but remove the pot from slug-prone lettuces once they fill out.
Constant vigilance against slugs is essential. They enjoy my homemade ale as much as I do, so beery slug traps dotted around the plot are useful magnets. Slugs also congregate beneath an old piece of rotting wood or plastic: check for slithery residents every few days.