This always makes me wince. I don’t think high uptimes should be celebrated. Has your kernel ever been patched or the services running restarted? Just installing the updates is not enough to secure your system you need to be running that new code as well.
Also, I get very nervous about touching those systems. You have no clue what state it is in. I have seen far too many large uptime server have their power go some day and are never able to boot again or don’t boot all the services back up as someone forgot to enable the service.
Nop, rather see them rebooted regularly at a non critical time so we know they will come back up. Or even better have a HA setup.