If your Magento 2 Blog search does not work, most likely the issue is in your theme that overrides original blog templates and layout files.
Try the next steps:
1. Make sure that you have the latest Magento 2 Blog module version.
2. Try temporary remove Blog layout XML files and template PHTML files from your theme one by one and run static content deploy. Once find the file that brings the issue, pay attention to it.