a) What’s PEP?
b) Large corporations usually have policies related to sponsorships, the most developed of which require that sponsored events bring them some exposure and are somehow tied to the company’s mission. As your experience seems to indicate, smaller and privately held companies are much more loose with their giving criteria and expectations.
With smaller companies, it may just be a matter of convincing the owner or someone else high up on the chain that your cause is interesting/worthy, etc. With larger corporations, you’ll need to tailor your ask to demonstrate that your cause meets their giving criteria (sometimes you can find these online, but if not, just ask their PR person or their corporate giving person). Ask yourself, “which companies will benefit from exposure (i.e. what kind of people are being attracted to your “event” and whose customers are they) and/or which companies are aligned with your organizations causes? Also, how can you increase the contributing company’s exposure during the course of the event to make giving more attractive?
Another roadblock with larger corporations is that giving is often budgeted and mapped out once a year, usually with some flexibility, but not much. So that big pie that you imagine might have a slice left for you has already been distributed.
Best of luck.