receiving mail during Exchange maintenance?

Absolutely. You're looking for a secondary MX (mail exchange) service. There are a variety of companies that and provide such a service. I like DynDNS.com's "Backup MX" service myself, but there are many companies who can provide such a service.

You could provide such a service yourself with a secondary mailserver on-site, but if you don't have redundant Internet connectivity to your office it probably makes sense to get this service from a third-party anyway (so that your email doesn't "go nowhere" if your Internet connection fails).

What you can do is either provide a backup MX record pointing to some front end smtp server (I used to do that with a linux box with exim) which is configured to redeliver your mail to the exchange server, or -why not- have that box in front permanently (as your public smtp server). The lightest servers will do really, so that solution should be in reach of any kind of organization.

Having a backup MX record and server is the way to handle this one. Other comments on this topic cover that well. One thing we've run into is that you have to have the same quality of spam-checker in front of your backup MX server, as spammers frequently specifically use backup MX servers under the assumption that their anti-spam is not as effective.

This is one of the reasons we "outsourced" our email virus scanning + spam filtering to one of those offsite providers. Not only does this remove what can be an intensive process somewhere else, and save your internet connection bandwidth by not having stuff that you're going to reject out of hand travel over your link, it also means that in the event of an outage any email is queued by them until your server can pick it up. Obviously this costs a bit but depending on how much email you get and how important email is to your business, it might be worth considering.

We used Messagelabs and have since moved to Mimecast, but really there are dozens and dozens of providers out there you could look at.