The most common reason someone would not receive an email reminder for the class is the email is being filtered by their email server to somewhere other than their inbox. Have the client check their spam and junk folders to see if the email is hiding there.
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Another reason a client might not receive a certain class reminder is due to the timing of their registration for that class. The registration reminder will send whenever a client registers for a class, whether 1 week before or 1 minute before class starts. The time-based reminders, however, will only send if the client registers ahead of that benchmark. For example, if you only have the 1-hour reminder turned on, and a client registers for class 20 minutes before class, they will not receive the 1-hour reminder message due to already being past this benchmark.
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Lastly, if contacts are not receiving their Livestream emails, you'll want to troubleshoot the Default Sending Profile and ensure you have a Default From Address and Default Reply-To address entered.