The Trinity study looked at 'safe' withdrawal rates from retirement portfolios. They found it was safe to withdraw 4% of a portfolio consisting of stocks and bonds. I cannot immediately find exactly what specific investment allocations they used, but note that they found a portfolio consisting largely of stocks would allow for the withdrawal of 3% - 4% and still keep up with inflation.
In this case, if you are able to fund $30,000, the study claims it would be safe to withdraw $900 - $1200 a year (that is, pay out as scholarships) while allowing the scholarship to grow sufficiently to cover inflation, and that this should work in perpetuity.
My guess is that they invest such scholarship funds in a fairly aggressive portfolio. Most likely, they choose something along these lines: 70 - 80% stocks and 20 - 30% bonds. This is probably more risky than you'd want to take, but should give higher returns than a more conservative portfolio of perhaps 50 - 60% stocks, 40 - 50% bonds, over the long term. Just a regular, interest-bearing savings account isn't going to be enough. They almost never even keep up with inflation.
Yes, if the stock market or the bond market takes a hit, the investment will suffer. But over the long term, it should more than recover the lost capital. Such scholarships care far more about the very long term and can weather a few years of bad returns.
This is roughly similar to retirement planning. If you expect to be retired for, say, 10 years, you won't worry too much about pulling out your retirement funds. But it's quite possible to retire early (say, at 40) and plan for an infinite retirement. You just need a lot more money to do so. $3 million, invested appropriately, should allow you to pull out approximately $90,000 a year (adjusted upward for inflation) forever. I leave the specifics of how to come up with $3 million as an exercise for the reader. :)
As an aside, there's a Memorial and Traffic Safety Fund which (kindly and gently) solicited a $10,000 donation after my wife was killed in a motor vehicle accident. That would have provided annual donations in her name, in perpetuity. This shows you don't need $30,000 to set up a scholarship or a fund. I chose to go another way, but it was an option I seriously considered.
Edit: The Trinity study actually only looked at a 30 year withdrawal period. So long as the investment wasn't exhausted within 30 years, it was considered a success. The Trinity study has also been criticised when it comes to retirement. Nevertheless, there's some withdrawal rate at which point your investment is expected to last forever. It just may be slightly smaller than 3-4% per year.