Hi there. First of all, thanks for trying Staatic to speed up and secure your WordPress site, and sorry to hear that you are having issues with the publication.
In order to find the cause of the stall, we need some more information. At which step does the publication stall exactly, and how many pages were crawled (or deployed) until then? You can find this information on the publication details page.
Also a screenshot from the publication details page, and diagnostics file would be helpful to troubleshoot the issue. The diagnostics file can be generated by going to /wp-admin/admin.php?staatic=diagnostics
and may be sent to [email protected]. It contains some environment information (feel free to open it in a text editor to verify).
Looking forward to your feedback.