First of all, if ProtonMail is not updating or you have not received any email, the first thing to do is verify that your internet connection is working well and try to use only a reliable connection as connectivity problems usually make email synchronization ineffective. Then, you can also log out of your ProtonMail account and observe this practice for a few moments before logging back in, which may assist in re-establishing the server connection.
You may also want to turn on the spam filter and check its proper function, as some emails may be unfiltered from the main inbox altogether. If ProtonMail is used through a bridge app and the configured settings are incorrect, making changes on either the client or ProtonMail itself can cause issues, and I would always recommend resetting any setups after making changes. Also, if there are problems with the Chrome browser, then there is a need to delete the temporary internet files or use a different browser altogether.
If none of these seem to solve your issue, you may need to get in touch with ProtonMail Customer Support, as such contacts are likely to show what the causes for not updating or receiving email properly may be, or account-related matters that are responsible for loss of email synchronization.
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