Earn it
Charitable causes generally seek donations from individuals, corporations, and foundations. They usually request a "gift," as the donor is expected to want to support the cause directly.
Some donors, though (mostly corporations and foundations), prefer that causes EARN their "donations" and not depend on handouts (gifts). Those donors may award challenge grants, offering to match the amount of money raised by a cause.
They are still contributing, but they are forcing the cause to learn how to earn money on its own. The cause will then become more sustainable and be better able to support itself in the future. Subsequent donations can then be used for growth, not for survival.
Race sponsors often share that philosophy, and provide something of value to events to help them earn money, like product, raffles prizes, hospitality venues, or premiums.
The race can hold volunteer parties, pay travel and lodging expenses for elite athletes (whose presence may increase publicity), provide a desirable goody bag, run print or electronic advertisements, or offer a slew of valuable raffle prizes.
Marathons often employ this same tactic. Instead of making a contribution to a cause, they'll sell it discounted entries which are then distributed to supporters who raise money for the cause.
The cause benefits by being able to offer something of value to people who might not otherwise have been attracted to the event, thus raising funds that would not have been available through traditional methods.
So, take advantage of sponsorship offers even if they don't include cash. Some things are just as valuable.