This wasn't on Linux, but on one of the old-school commercial Unixes - a customer had memory leaks in some of their daemon processes. They couldn't fix them for some reason.

So they invested in additional swap space, let the processes slowly grow, swap out leaked stuff and restart them all over the weekend...

I wrote a chat server back in the 2000s which would gradually use more and more memory over a period of months. After extensive debugging, I couldn't find any memory leak and concluded the problem was likely inside glibc or caused by memory fragmentation. Solution was to have a cron job that ran every 3 months and rebooted the machine.