Hi Justin -
Yes, a loss on your schedule E could potentially affect your financing on the next home if you don't have enough outside income to cover the DTI requirements. If you are purchasing a NOO, you can use 75% of the projected rents on that property to help offset your debt load.
Lenders will look at your net P/L on your schedule C to determine the income generated from the property. However, there are multiple addbacks to be included. Mortgage interest, homeowner's insurance, HOA fees, and property taxes are three of them. These will already be included in your DTI, so will not double count against you. The potential big one that can be added back in and not count as loss is Depreciation. Lastly, Renovation, and non recurring repairs can also be added back in. Be prepared to show documentation to prove to the Underwriter they are indeed non-recurring expenses that took place.
Simple scenario: let's say your schedule E shows a net loss of $20,000 for the year. But there's $15,000 in depreciation, and another $15,000 in non-recurring expenses - makes your net profit +$10,000 rather than -$20,000.
Hope that helps!