Their free cash flow (profit plus depreciation minus capital expenditures) well exceeds their dividend. In their latest quarter, they had ~$6.5M of income, ~$21.6M of depreciation (a non-cash expense), and about $10.6M of CapEx. Their dividends were almost covered by the difference between the depreciation and their CapEx spending alone. Throw in their income and they had enough cash left over to pay down a couple hundred thousand dollars in debt, too.
Also, they had another $7+ M in income adjustments for the quarter, so this is additional cash flow above and beyond that above. (Income adjsutments include non-cash expenses like stock options.)
Bottom line, the large depreciation expenses are from CapEx that was spent years ago in wireline telecom companies like CNSL. Current stockholders are getting the benefits of the depreciation of these old assets via the positive cash flows they generate every quarter. These kinds of telecom companies also do not have to spend on infrastructure CapEx like the wireless telecom companies do. Over time the wireline companies revenues are declining, but their DSL and TV services over their fixed lines will offset some of the "plain old telephone service" revenue decline.
And when companies like CenturyLink (CTL) buy others (like Embarq) or Windstream buys Iowa Telecom, they get to start the depreciation clock over again on the hard assets they acquire. They get another ~30 years' worth of depreciation to shelter profits from. Great news for us investors who like the dividends from the positive cash flows.