Trimble Connect user with personal account should be able to create 1 new project without receive warning message. For this case, would you be able to submit ticket to Trimble Connect support channel by email firstname.lastname@example.org? So that we can follow up with you further on this issue.
If you can't save model by creating new project on SketchUp Free app, try click model menu (Folder icon) next to save button and select "Download". Model will be downloaded as SketchUp file to your local drive and get backup. Hope this could help.