OS X Mail: What circumstances are there were Mail rules could be delayed or not invoked I have some rules set up in OS X mail to forward important messages (by containing a particular string in the subject) as MMS text to my phone.

Obviously when the machine is off, internet is down, or Mail isn't running, the rules will not work, but I want to be certain I am considering all other circumstances where rules might not be forwarded.

Will OS X Mail forward messages when the computer is asleep, and are there other factors or situations I need to consider?

Running OS X High Sierra.
macOS mail app only runs rules when it’s fully powered up (not just power-nap checking mail) and connected to the internet. You would need a server side rule processing provider like Outlook / Exchange / O365 to have rules trigger when your local mail client isn’t running to have a robust mail rule engine to work 24x7.