First off, I'd question the premise a bit. There are plenty of investors that have large real estate holdings and correspondingly large loan amounts and expenses that are constantly verging on bankruptcy.
Large investors have the benefit of diversification and professionalization.
Diversification If you own a single rental unit, you have a great deal of idiosyncratic risk-- you might find that you've got a great tenant that pays on time every month for a decade and leaves the place spotless or you might find that your tenant lost his job and can't pay rent for several months while you try to evict him and then find that you're on the hook for several thousand dollars in repairs. If you're a small landlord, one bad tenant can wipe out years of income. If you own a hundred rental units, you can reasonably bank on some percentage being empty, some percentage being behind in rent, etc. and end up with a much more consistent return.
Professionalization If you own a single rental unit, the tenant probably calls you directly when the water heater dies. You then have to drive out, take a look, fix it or call a plumber, etc. That's a lot of hassle to deal with in the middle of the night. If you have an apartment complex with a hundred units, on the other hand, you'll have handymen on staff to take care of most maintenance problems, management to bring in plumbers when needed, and contracts with plumbing companies that give you a discount for sending them a consistent amount of business. If you have one rental unit, you have to learn how to advertise, how to screen tenants, how to deal with maintenance issues, how to evict someone, etc. yourself and you probably won't be great at any one of them. If you have a hundred rental units, you can hire people that specialize in each aspect.
Of course, there is also the simple issue of skill. People that are good at being a landlord tend to make more money than those that aren't great at it. People that make more money as a landlord tend to buy more units than those that don't make as much money. So, over time, people that are good at being a landlord end up with more units than those that aren't so great at it.