If you have a non-durable subscriber and you use the JMS engiine (property of the UM channel), then any messages published while the subscriber is disconnected will be discarded. If you want to ensure they are stored in UM and delivered when the subscriber comes back online, then you should use a Durable Subscriber. That is what Durable Subscribers are designed for.
If you use the Default engine for the channel, then messages will be stored on the channel until purged, either explicitly or through TTL or capacity settings. This is irrespective of subscribers having received the messages.
Whether messages stored on the UM server survive a server restart, is determined by the channel type. If the channel is Persistent, or it is Mixed and messages are sent as Persistent, then messages are stored on disk and will still be there after a server restart.
From your questions, it sounds like you should be using Durable Subscribers in combination with persistent messages over a Mixed channel. That will ensure that messages are stored while a subscriber is offline and will be guaranteed to reach the subscriber eventually, even after UM server restart. This is a very common pattern and doesn’t require extra coding, resubmission, ack checking, etc.
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