Most older, local, small businesses in small to medium markets in the US will never be growth businesses. They're treading water businesses after the market is saturated (some can be very profitable of course).
Being technical about it, a business may keep up with inflation by raising prices, and show nominal growth.
Look at the revenue of a liquor store, insurance business, or tv / radio station, in a healthy but smaller settled market. No market growth, little to no business growth, but the businesses aren't likely to disappear either. This is a very common scenario, there are millions of US businesses in this situation.
More accurately: they're earning normal economic profits. This assumes that economic activity is normally profitable, which isn't unreasonable in certain circumstances, though it's not guaranteed.
Driver of what? Maybe a dry-cleaner or cafe is happy with the size they are, because expanding would involve turning the business into a chain or something else the owner doesn't want.
Not that economic orthodoxy is a good measure of reality, but there is a theory of the optimum size of a firm that will determine its size.
There are natural monopolies which grow without apparent limit, or rather, whose growth is constrained only by the total size of the market, rather than some lower bound. For these, there's always the capability of adding additional profitable production.
For other businesses, there are natural constraints on scale: a regional market or operation which can only sustain so much business, high scale-related costs, etc.
As two canonical examples, telecommunications scales quite well with scale, and in the history of telecoms we find a long history of monopolies: Western Union in the telegraph age, AT&T in the telephony age, and now Comcast in the broadband era. Once you've got cables strung, your primary limitation is last-mile wiring. But it's the long-distance and total bandwidth capacities which give you maximum value.
Concrete is a counterexample: there's a limited local market (whatever local building activity will support), and your transport costs are very high: concrete is heavy stuff. Concrete tends to be a pretty localized industry, though it might be possible for a single firm to develop out of what are essentially multiple regional markets.
Growth, where possible, profitable, and sustainable for a business, is often pursued, but it's not a necessary condition for success.
An instant counterexample I thought of is a non-profit.
Individuals working there are always excited about personal empire building of course, but if the stated community need is being met, well, that's good enough, in fact if that need is dropping that can sometimes be awesome.
Stereotypical orphanage or red cross or homeless shelter.
Churches are another business that often is fairly steady state plus or minus population changes and inflation.
Of course non profits can experience explosive growth, my credit union is a non-profit coop and since the nationwide banks have gone into decline with exploding fees and imploding services, the CU has recently had exploding growth rates. Which admittedly has a lot more to do with external societal factors than internal goals.
Being technical about it, a business may keep up with inflation by raising prices, and show nominal growth.
Look at the revenue of a liquor store, insurance business, or tv / radio station, in a healthy but smaller settled market. No market growth, little to no business growth, but the businesses aren't likely to disappear either. This is a very common scenario, there are millions of US businesses in this situation.