No, the e-vignette does not automatically renew and no such option is offered.
That means you always have to purchase a new e-vignette each time the validity has expired.
Related articles:
How long is the Czech e-vignette valid?
Where can I check the status of my Czech e-vignette?
Where can I buy the Czech e-vignette?
What vehicles need a Czech e-vignette?
What different types are available for the Czech e-vignette?