Yes, it is possible for seedlings\plants to require water every day. They need to be watered when ever the media has adequately dried out, however, it should not be allowed to dry out completely. The sick looking one in the second picture (which appears to be in a coco coir pot) looks like it is getting too dry. How deep was the container?
You generally cannot put a strict interval of frequency or volume as to watering; when you water, water thoroughly and then do so again whenever the containers have lightened up considerably, but are still semi-moist. Seedlings especially you do not want to allow to dry out completely. Several factors determine how frequently you're going to need to water, including the use of a fabric or natural fiber (coir, peat) pot. It is normal to have to water more frequently as roots grow into the medium.