When Plug in Git imports the changes made to the theme in Shopify and there are merge conflicts the theme changes with not be merged into master.
Instead, the theme changes will stay on a branch called current-shopify-theme and Plug in Git will create a pull request where you can manually resolve the conflicts.
Automatic deploys are stopped until the merge conflict is resolved. New changes will continue to be imported to GitHub but they will be synced to the current-shopify-theme branch instead of master.
Once the merge conflicts are resolved you can manually merge the PR into master. Then the automatic deploys will resume.