No. For cash basis taxpayers (which is almost everyone) income that you did not receive is just that -- income you did not receive. You can't take a deduction because you can't subtract something that was never part of your income to begin with. Your taxes are lower because you had less income. A refund would be money you paid back from money you had already received and reported as income.
For certain taxpayers who use accrual accounting, they book the revenue when a contract is signed, so accrual taxpayers would take a deduction for a cancelled contract. But remember, they are subtracting a payment that was never made from income they already reported (even though they hadn't been actually paid yet).
Expenses more than income is fairly normal, lots of businesses operate at a loss. Your loss may be deductible against other income or it may carry forward to offset future profits. If you make a loss in more than 3 out of 5 years, the IRS will look to see if you should reclassify your activities as a hobby. But one or two years of losses are unfortunately normal.
