Hi,
I am sorry to hear that you are missing some emails. There are a number of troubleshooting steps we can take to find out why. If there is an error message that occurs, please provide that error message in your response.
Are you using IMAP or POP3? This will determine if you can retrieve the old emails off of the mail server or not.
If the issue occurs in Thunderbird on a new computer and you still have access to the old computer, the old profile folder can be added with these instructions. More info on backing up and restoring profiles is also available in the Move Thunderbird data to a new computer and Profiles support articles.
To prevent this from happening again and when using IMAP, you can check "Synchronization & Storage" in the account settings for the affected account and click the "Advanced" button to see if all of the folders are selected to be synchronized and kept on the local computer. More info on this can be found in the IMAP Synchronization article.
If the issue is about not receiving any email, please see the Cannot receive messages article for more help.
I hope this helps.