Satellite messaging is not like cellular messaging. With cellular, it's almost instantaneous when you have service. With satellite messaging, you don't maintain a constant connection. We rely on brief connections to send small bursts of data. The whole process is generally quick, but it can take several minutes even in good sky visibility. Low orbit satellites are constantly moving across the sky. This is why the signal LED light is constantly changing from green, to yellow, to red. This is NORMAL. When the LED is green, it will send or receive pretty quickly.
You can increase the signal strength by orienting the device straight up and by not covering or obstructing it with anything. If there is no signal LED then the device is on standby to preserve the battery. That does not mean there are no satellites visible.
The device will wake up when you send a message or press the power button once quickly. Every 15 minutes it will wake up to check for new messages. You can also do a mailbox check to check for messages manually.