This is a nice question, Name the insect who does not sleep? I have two subject before related to insect its, Entomology 101 and Entomology 102, my instructor before told as to collect the different kinds of insect. So I started to collect for different kinds but then they told us that its is better if we will caught insect during at night so I tried to get lamp and I went to the garden. Then yeah!!! A lot of insect flying like moth, grasshopper and beetles. So I want to say this kind of insect doesn't sleep.
All insects does sleep but they do not look like that they are sleeping. Insects do not have eyelids like we have. Quiescent period is the time when an insect sleeps. It can be a day or night time. For more information on insects please visit the following link.
Termites...they also work for 24hrs
They do sleep of course. Usually, most of the living life does require sleep to regain the energy needed.