Chervil should be treated much like parsley. They don't like being transplanted, so seeds should be sown in situ (where you want the adults to end up). Most people sow seeds in tiny pots, which works only for a short time once the plants begin to grow. The roots don't have much room to spread, and not much in the way of nutrients to get at, since the pots are small and the roots are scrunched. So they tend to get overwatered - and I think this is probably the 'root' cause of your problem.

Also, start harvesting your chervil (or parsley) at a fairly early stage, always taking only about one-third of growth at any one time, then waiting until it regenerates before harvesting again. Pick it and pick it and pick it. It's a floppy plant anyway, and the older leaves do die off if not removed. It's a fast grower, and can reach maturity within 6 weeks - so the dead leaves are probably dying of old age.

If the seeds are old, they may fail. I used a lot of pea seeds that were a few years old. Every time I planted 20 or more, I would only see 4-5 sprout. The next year it was down to 1-2. I tossed out all the peas and bought some fresher seeds for this spring. Same with corn and a few other veggies. The same is true for most all seeds. A good seed staring soil can also help. Natural Beginnings, offered by Gardens Alive is a very good seed starter and I have always had goo luck with it. If there is a damping off issue, they also have soil treatments to prevent most problems seed starting can have.

The book Seed to Seed by Suzanne Ashworth is an excellent reference for seed starting and saving. It says that chervil seeds retain a 50% germination rate for seeds saved 3 years or less in optimum conditions. (Ksrogers, same noted for garden peas.)

As previously mentioned, it says chervil is usually direct sowed, germination temperatures of 50-65 degrees F, and 7-12 days germination.

FataMorgana

If the seeds germinate and sprout then the seeds were still good and should produce healthy plants. I suspect that the seedlings may have 'damped off'. This is a very common disease problem caused by a soil born pathogen. If the soil stays too wet for too long the pathogen will cause the stem to collapse right at the soil line and the plant will fall over dead. Provide your new seedlings with good air circulation so the top of the soil dries out slightly between watering. Also good strong light about 12 to 14 hours per day from an artificial or a combo of natural and artificial light will help seedlings become strong and healthy. Seedlings should be supplied such light from the time they first emerge from the soil. Fertilize half strength once a week. Mature plants prefer cooler temperatures than most herbs so are great spring and fall crops where it is really hot in the summer. As for transplanting, I have transplanted thousands of seedlings with great success for over ten years as my father did for 25 years before me. Always make sure to harden off your seedlings (usually a week long acclimating process) when transferring seedlings from inside to outside before planting them out.

My peas had about a 15% yield after 5 years of storage. All were tossed out. Gardens Alive now offers a new product that is useful for seeds that tend to succumb soon after germination. IT not only reduces damping off problems, but many other soil related problems. I always start seeds in a soilless mix which is sterilized so nothing but the seeds will prosper. I also do not use peat pots, as I much prefer a plastic pot for my seed starting. Rosemary is a difficult seed start, but mine germinates at 99% success rate, and there has never been a single loss in any of my plants once transplanted either. I always place my plant in my small greenhouse prior to any planting outdoors. Not only does this reduce plant stresses, but also gives you plants that will not get sunburn or be attacked by leaf eating bugs just after they are planted.