@ Ryan
When WordPress updates plugins it downloads and decompresses the plugin to a temporary folder on the web server. Where that location is really depends on the web host, so, I could not tell you where it is at. The issue is for some reason After WordPress downloads and decompresses the update it is unable to copy that file to the plugins/connections-widgets folder. The error is generated from the file in the temp folder, not the file in the plugins/connections-widgets folder.
So, it seems that WordPress is able to retrieve and decompress the file just fine but something on the webserver is preventing either the old file from being deleted and causing the copy fail or the temp file can not be copied. Either way this seems to be a web server issue that you’ll have to contact your webhost and ask about.
The only thing I can suggest is to deactivate the plugin, delete it and then manually reinstall it again (the updated version). You will not lose any data and the widgets you’ve configured will remain intact.
Hope that helps, let me know.