Does it mean my distro is broken (it's a custom distro for a board I'm using, it could easily be buggy)? Can I tweak this behaviour?
Yes, that sounds broken. The Filesystem Hierarchy Standard mandates that
This directory contains system information data describing the system since it was booted. Files under this directory must be cleared (removed or truncated as appropriate) at the beginning of the boot process.
/var/run is a RAM disk, there is no reason that rebooting will affect any of its contents at all. Most well-behaved applications that drop files there will (try to) clean up after themselves, but other than its generalized use-case there is nothing special about that directory on your filesystem as compared to most others.