Look at it this way - if UAL and DAL abandoned their regional connections tomorrow, SKYW would still be there to fill the need in the market. And they would be totally stupid to give up a service that feeds regional passengers into UAL's and DAL's main intercity routes. Demand exists - SKYW provides part of the supply.
The only risk is if UAL or DAL took the business from SKYW and gave it to another regional carrier. But why should they? DAL has deliberately diversified their regional service providers since the Comair problem a while back; SKYW has proven itself an efficient, reliable partner for the majors.
Supply and demand - SKYW meets a need in the market and does it very well. That's why UAL and DAL (or another major if UAL stops flying, which is EXTREMELY unlikely even under Chapter 11 BK) will contine to fund SKYW's high profits.