A syslog server collecting logs does not show logs generated during the reboot, even after connectivity is restored post reboot logs are still not showing in the server.

Logs while rebooting a device will not be sent to the server, instead they will be saved locally in the device as per design.

You can use some commands to review important logs after a reboot process:

show chassis hardware

show chassis alarms

show system alarms

show system boot-messages

show system core-dumps

show log messages

show chassis fpc detail

show chassis environment

https://www.juniper.net/documentation/us/en/software/junos/cli-reference/topics/ref/command/show-system-boot-messages.html

https://www.juniper.net/documentation/us/en/software/junos/cli-reference/topics/ref/statement/syslog-edit-system.html

You can also use scp protocol to move any required log into a host or server:

https://www.juniper.net/documentation/us/en/software/junos/cli-reference/topics/ref/command/file-copy.html