A couple of non-profits I do some IT support for uses iMIS (try www.advsol.com). One has about 20 users and 1500 members, the other has 50 users, several thousand members, but there are a bunch of other organisations which scale much higher.
It's not cheap, but we've found it to be very effective, and relatively easy to maintain. It's got a pretty decent user base, so there are a bunch of 3rd party addons. It works well as a backend to a public website, so you can have your members updating their data, booking events, etc over the web.
It's all pretty standard .NET/SQL stuff, so it's pretty easy to implement and come up with a DR strategy too. The product has been relatively bug free, and even the user interface is pretty good.
The biggest issue is documentation. Although the generic end-user documentation for each module is quite good, you'll need to incorporate some budget for implementation-specific end user documentation. We also found that our implementers provided completely inadequate technical doco - you couldn't possibly rebuild the system going by the documentation, which makes disaster Recovery an issue. Expect to have to hassle your provider for usable doco.