Hosting an Efficient Multisite with Many WPMU plugins

Our Dreamhost dedicated server has 2GB RAM, running apache. We have a WP multisite using plugins buddypress, domain mapping, classifieds, event manager, membership, gravity forms, google maps, among others. It's not a multi-network, just a multisite with separate buddypress networks.

The main site has almost no users. We have 700+ users on sub site which has seen about 5,000 page views or so a week for the last few weeks. The site (and network) goes down every few days for 1-2 hours at a time. We can't login or FTP in, our only recourse is to restart the server.

Dreamhost has told us PHP memory limit is the issue. We recently started using the W3TC plugin for caching, which is helping. Still experiencing issues. Recently upgraded PHP to 5.6 with FastCGI.

Can you make suggestions on preventing our site from going down?

We are running registration for an open studios arts festival that will have a lot of logged in viewers leading up for registration, and during the week of live events in early June. We need to make sure we can keep this site up and running so visitors can find the locations they are seeking on our maps.

Alternatively, we are thinking of upgrading to a 4GB Ram server, but if we can make this installation more efficient to handle our traffic that would be best.