If you just want to receive emails, then it depends how long is your downtime. Smtp requires that the sending server makes several attempts if the first failed, so if you are only off for a few minutes to a few hours, you will get your emails, just delayed. If full day downtime then this is not a viable solution.
If you need to send emails, then you kind of have to host your server in a datacentre. A cheap VM should probably be a good solution for a first attempt. You will still get downtime occasionally (update OS, update mail software, problem with your hosting provider). A cheap solution is to set up a failover server at home since it is only to receive emails while the primary server is down, with a lax retry policy (up to a few days).
If you want to be sure your mail gets to someone else, things are going to be more complicated than setting up an SMTP+IMAP server combo, and after dealing with it in the past for work I'm happily outsourcing the pain to fastmail nowadays. :)
Almost every mail server retries for a few days, so you'll get your message, just late. Those few mail systems that don't retry have issues with greylisting - and unless you're fond of stories about Nigerian princes in distress, you're going to use that as the first anti-spam measure anyway.
Then you've chosen a bad service provider(s) to host/colocate/peer with.
Actually, you should notice this situation pretty much immediately you're online - because most likely your IMAP server would be down - and every single email client I've used had started to display warnings.
If you have more complex setup with separate MTA so your IMAPd may be online while your STMP service's unreachable, then you should set up monitoring system and deliver alerts either using local delivery or any out-of-band mechanisms (like SMS).
Also, you can set up a backup MX. Or two. Or more. Email has failover/HA since forever.