I run my own mailserver too for private use. I make use of a DNS provider who also provides backup SMTP service.

Basically it adds another address as alternative for delivery for your domain. That server is configured to forward the mail to your primary server or hold it until it comes up again.

Works great, and you could even use it as a spam filtering option, since legitimate servers should only try the first server, but a lot of spammers use the second one thinking that it probably has less spamfiltering or something.