Running out of memory sometimes happens on swap-less VPSes, and it seems Webmin (together with its twin, Virtualmin) are among the first processes to die in out-of-memory cases.

Setting up a little script to check for and restart Webmin if it is no longer running is a pretty simple (workaround) solution – but should never replace the proper procedure of adjusting the settings or upgrading the VPS to avoid running out of memory in the future.