I am using a free version of Hubspot and have had no problmes with it up until the last week or so.
I have created a couple of contacts that despite having the first one or two emails synced from my gmail - new messages no longer seems to appear in hubspot.
The email address has not changed and they both match too.
I would recommend confirming that when you are sending the emails you are checking off the log option. If the issue persists and you can send along screenshots of emails that are sent with the bcc address in the sent email and a link/screenshot to the contact record.