There's seems to have been downtimes maybe 1-3 times a day. This seems to be a glitch in web server configuration, perhaps an incompatibility with some php application or a bug somewhere. It has been difficult to track down because there's nothing in any logs that would give a hint what causes it. Hence I've made some temporary alterations to web server configuration to revert it back to what it was before Sunday. Currently it performs slightly slower but hopefully it also stops these downtimes.
I'm in the process of preparing and testing a complete overhaul of the web server configuration, which theoretically should improve both compatibility and performance without sacrificing security. Depending on how quickly I can get the new config tested in a virtual machine and whether this temporary config works, there will be possibly 30 minute downtime coming sometime during Friday-Sunday time frame. Once done, I can only hope that'll be the end of downtimes.
There was another downtime earlier today/late yesterday where our ISP made some network servicing.