The resources they are worried about are the number of file requests and the bandwidth, which if you are worried about running out of a Terabyte of server space, you might be smokin'.
They are outright canceling your contract or they want to bump you to the next service/cost level?
I use Network Solutions hosting, not the cheapest, but they make running multiple domains painless. I don't know what Rick uses and am too lazy to whois it. I'll let him explain, but this board is an order of magnitude under what you need if you are getting kicked for. You want cheap high performance, where this site can get along with cheap low limits. Apples and oranges.