It was just attacked by hackers a few months ago, no to mention all the lawsuits they've been getting, and cost of maintenance of TERABYTES of data. They really need the funding to survive.
Edit: Missed the FOSS part, but still, its worth mentioning. archive.org is not an open source software, but they are a non-profit doing something that benefits all of us. And they are transparent about how they operate. More like a "Free and Transparent Community Service", rather than "FOSS". And not to mention, the many FOSS software they could preserve in case they stop getting maintained, so they could get picked up later, and not be forever lost. It goes hand-in-hand with the philosophy of FOSS: benefiting society.