I make the assumption that you’re running PHP 5.3 (the currently newest PHP version officially available in CentOS 6) or perhaps PHP 5.4.

The switch can, theoretically, be done on live system – just prepare yourself for a bit of hiccups here and there (or perhaps even serious downtime).

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.