They only will get one reply until they read the thread again. If they only visit the forum home page, or read other threads, they won't get a new alert or notification. They have to view the thread again.
This is the "break" from how vBulletin did things. In vB, all you have to do is visit the forum and all "can send notification" flags are reset for all "subscribed" threads/forums.
I am having
@Xon modify
https://xenforo.com/community/resources/persistent-alerts.4962/ so that you can offer the old vB functionality. Peristent Alerts currently allows you to continue to get notifications on watched threads, regardless of even visiting the forum - but to some, that might be a bit much. That's why I pushed to get the vB notification functionality added into that addon
regarding the conversation notifications, they should be getting these regardless of having read the convo...that works differently. I would have them check their preferences
https://xenforo.com/community/account/preferences and make sure "Receive email when a new conversation message is received" is checked. If it's not that, then they should check spam/junk folders. If they are using gmail, hotmail (msn, outlook, live, etc), yahoo, or AOL, there are ways of "whitelisting" the forum's email address to prevent any messages from going to junk. Also this is something you must do online, in the webmail. Some people thing that adding an email address to the "VIP" on their phone does it, or a setting on their email client does it...no, it doesn't. The filtering has to happen at the source, online.
I have example tutorials I made for each of these services:
https://www.algaescrubbing.com/threads/attention-yahoo-e-mail-users.822/
https://www.algaescrubbing.com/threads/attention-gmail-users.824/
https://www.algaescrubbing.com/threads/attention-aol-e-mail-users.823/
https://www.algaescrubbing.com/threads/attention-hotmail-or-any-microsoft-e-mail-users.821/
If they are using gmail, and not downloading to an email client, it's possible that the forum emails are getting pushed to the "promotional" tab. I shut all these tab views off so I don't have that problem, but I've been told it happens.