Nah. If there's anything the server we're using has, it's space. I've uploaded DVDs to it without hassle. (Getting them back, that's the tricky part.) It is a lower-end host, by which I mean it isn't branded to host millions of people a day, and it's more than just my account on the same server. We share a connection and server with several customers (as well as a few other sites of my own). If another site gets a spike in traffic, we sometimes feel it. They're also in the process of frequent upgrades, and so we get those now and then.
But, as forums go, we're incredibly small. We use about 2 GB of bandwidth a month, and have yet to breach more than 20 people on at the same time. I know there's smaller out there, but we're definitely on the lower end of those that are actually active. I can't really picture upgrading when we're already doing better than most. (Ad free LotN, baby!)