And, upon being told that they have no ability to increase it, and them suggesting that you move to a larger hosting plan - begin investigating alternative hosting providers.
You normally see that with a shared hosting account - and short of upgrading to one of their higher levels (which usually doesn't get you that much for what you pay), there are better alternatives out there. Depending on how busy your site is, you may have progressed to the point of needing a VPS or a custom shared hosting provider (
@xenBoost Mike for example - and no, I'm not associated with him - I've just seen several people that have used him that are happy with his service).