Do you think it is important for a 4-year-old kid to be regular in school? I often let my kid skip if she is very sleepy or don't feel like going.

She's just 4 years old and not going to school for a day is okay. But do not make a habit of it because if she's used to it you will face problems when she reaches higher classes. If the reason for her missing school is because of feeling sleepy then you need to adjust her sleep pattern and timing. Try and avoid skipping school for trivial reasons.