No, online stores do not automatically delete eBooks if they are not purchased.
You remain in control of your eBook and can decide how long it remains for sale.

In general, your eBook will remain online until you actively remove it. Unless you set a specific deletion date when publishing to control availability. Note, however, that stores can remove eBooks that violate their policies.
Stores can also reject new releases if they do not meet certain criteria. The final decision on availability rests with the individual store. Check their policies to make sure your eBook meets their requirements and is well presented.