Is there any reason deflation would reduce profits? Profits are the difference between input and output prices. So profits would only fall in those industries where output price fell faster than input price.

Is there any reason deflation would reduce profits in all industries rather than just some?
For some models, deflation makes consumers save more, because they expect one unit of money in the future to buy more goods than one unit now. Consumption falls, so revenue and current profits fall. 

The fall in demand and profit may have feedback effects: less investment, less innovation. 

In general, depends on the model you are using. In a static model with homogeneous firms, the real profits may stay unchanged.