Simon 5 is coming soon!
Simon version 5 is currently in beta testing. It is a massive update, introducing a much-requested feature: syncing the Simon data between multiple Macs, plus a Simon Status service, a Link Checker filter, improved Find filter, iMessage and Speak Error notifiers, a new app icon, and much more.
Important: please note that Simon 5 requires a minimum of macOS 10.12 (Sierra), and will be a paid upgrade from Simon 4 after the beta. Purchasers since September 1, 2020 automatically get a version 5 license (that also works in previous versions).
Re: include specific time/date checks in checking options
[Sorry for the delay in replying; I'm on vacation in Washington, DC this week.]
Simon includes a scheduler to enable you to perform checks at the desired frequency. You can also use the auto-pause settings to avoid checking when a server is known to be offline (e.g. a periodic reboot).
In the future I plan to add more scheduling options, to enable you to specify specific dates or times. But in the meantime you can do most of such scheduling with the auto-pause options.