Can missing several nights of sleep in a row cause your period to come late?

Yes it can..but preg. I would check a pregnancy test to make sure, but women with ovulatory cycles have an internal-internal clock called circadian cycle, which is related to/control sleep. So, signifincant sleep disruption can interfere/disrupt mentrual flows as well. If you are interested in more detail..Follow this link : www.Ncbi.Nlm.Nih.Gov/pubmed/17383933---have fun. Consult doc if you are concern. And good luck.
Maybe. There are lots of reasons why your period could be late. The most common would be that you didn't ovulate that month. And while we do see an occasional missed or late period in women with extremely stressful life event, there's no direct way of knowing if your lack of sleep caused a delayed menses or not. If your period is late and you are sexually active, first consider the pregnancy.